@Olivia Queen - "Using whether is far more common" - Here, Grammar-Monster was only referring to "whether/if ... or ..." constructions, as in "She didn't know whether to stay or go".

In normal indirect questions, "if" is "far more common", even in written English:

Netspeak - "He asked me if" - 78,000, "He asked me whether" - 5000
Ngram - "He asked me if" - 0.0000190%, "He asked me whether" - 0.0000020%
British National Corpus - "He asked me if" - 37, "He asked me whether" - 5

Incidentally, this question wasn't really about using "if" or "whether", but the use of "that" instead of either.

Incidentally, I somewhat disagree with those earlier commentors who see a difference in meaning between the two, or say that 'in' is followed by a verb, and 'with' by a noun.

Both 'in' and 'with' are prepositions, so the only verb form that can follow either is a gerund (-ing form), which is in fact a verbal noun, rather than a verb per se.

While Ngram certainly shows that before gerunds, 'in' is nearly always used, it also clearly shows that 'in' is preferred before standard nouns as well.

And it also shows that while 'in' before gerunds is still way in the lead, 'with' before gerunds is increasing in use, at the expense of 'in', in American English., at least:

http://books.google.com/ngrams/graph?content=assist+in+drafting%2Cassist+with+drafting&year_start=1800&year_end=2008&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cassist%20in%20drafting%3B%2Cc0%3B.t1%3B%2Cassist%20with%20drafting%3B%2Cc0

At Netspeak, the percentage of 'assist' followed by 'in' is 16.3% , compared to 6.7% for 'with':

http://www.netspeak.org/#query=assist+*

And 'assist in the' gets 5.1 % to 1.5% for 'assist with'

At the British National Corpus there are 541 instances of 'assist in', compared with 167 of 'assist in'. While many of those with 'in' are followed by gerunds, many are also followed by standard nouns:

"the civil servants he appointed to assist in the work"
"a suggestion from the Ministry of Supply to assist in the production of railway bridges"
"About the only contribution information technology can make is to assist in the compilation of cricket statistics. "
"Numerous tests are available to assist in the systematic assessment of a wide range of grammatical abilities"

Similarly,while the majority of instances of 'assist with' are followed by nouns, there are also quite a few followed by gerunds:

"Volunteers are welcome to assist with staffing of the City Varieties"
"where one is merely allowed to assist with abseiling a small group down a short drop"
"Guides will assist with the serving of tea or coffee and biscuits"
"a variety of methods have been evolved to assist with coping with them."

Everything points to the same conclusions:

'assist in' is by far the most common when followed by a gerund, but 'with' is also possible.
'assist in' is also more popular when followed by a standard noun, but the difference here is not so large.
All these sources suggest that 'in' is more common in a ratio of about 3.5 to 2

Sorry, that Ngram address didn't work. Go to http://books.google.com/ngrams and enter:

assist in the *,assist with the *

@MD - Both are correct, but "assist in" seems to be the most popular. Learner's dictionaries, for example, allow both, but most of the examples they seem to give are with 'assist in'. Incidentally, learner's dictionaries are rather better at giving this sort of information than standard dictionaries:

"assist in/with something" - Oxford Advanced Learner's Dictionary
"We are looking for people who would be willing to assist in the group's work."

"assist in/with"- Macmillan's Dictionary
Several top landscape designers assisted in the creation of the garden.

"assist (somebody) with/in something" - Longman's
You will be employed to assist in the development of new equipment.

"assist the police with/in their inquiries (UK)" - Cambridge Dictionary

The American Merriam-Webster's Learner's Dictionary gives these examples:

" Another doctor assisted with the operation."
"Federal agents are assisting with the investigation."
"She assisted in making the decision."
"The cream assists in the prevention of skin cancer."

At Ngram, the ratio of "assist in the project"to "assist with the project" is about 3.5 : 2. In general, it puts "assist in" quite considerably in the lead, and this graph also shows that both 'in' and 'with' can be used with the same words, for example "assist in/with the development", "assist in/with the preparation" (the most common collocations):

http://books.google.com/ngrams/graph?content=assist+in+the+*%2Cassist+with+the+*&year_start=1800&year_end=2000&corpus=18&smoothing=3&share=&direct_url=t2%3B%2Cassist%20in%20the%20*%3B%2Cc0%3B%2Cs0%3B%3Bassist%20in%20the%20defence%3B%2Cc0%3B%3Bassist%20in%20the%20work%3B%2Cc0%3B%3Bassist%20in%20the%20formation%3B%2Cc0%3B%3Bassist%20in%20the%20development%3B%2Cc0%3B%3Bassist%20in%20the%20execution%3B%2Cc0%3B%3Bassist%20in%20the%20establishment%3B%2Cc0%3B%3Bassist%20in%20the%20production%3B%2Cc0%3B%3Bassist%20in%20the%20process%3B%2Cc0%3B%3Bassist%20in%20the%20maintenance%3B%2Cc0%3B%3Bassist%20in%20the%20preparation%3B%2Cc0%3B.t2%3B%2Cassist%20with%20the%20*%3B%2Cc0%3B%2Cs0%3B%3Bassist%20with%20the%20development%3B%2Cc0%3B%3Bassist%20with%20the%20work%3B%2Cc0%3B%3Bassist%20with%20the%20preparation%3B%2Cc0%3B%3Bassist%20with%20the%20other%3B%2Cc0%3B%3Bassist%20with%20the%20cost%3B%2Cc0%3B%3Bassist%20with%20the%20provision%3B%2Cc0%3B%3Bassist%20with%20the%20design%3B%2Cc0%3B%3Bassist%20with%20the%20harvest%3B%2Cc0%3B%3Bassist%20with%20the%20construction%3B%2Cc0%3B%3Bassist%20with%20the%20implementation%3B%2Cc0

@jayles - Fair enough.

In history classes at university we had a lot of discussion as to whether certain changes that took place in the UK after WWII, such as the rise of consumerism and the new availability of certain household appliances, constituted Americanisation, or whether it was simply modernisation, which had started in America.

I'm sure it's much the same with language: because a lot of social and technological change first appeared in the US, not to mention the whole idea of business as a 'science', and the cultural domination of Hollywood, we are bound to have taken on a lot of words which though they may have originated in America,are simply part of our modern lifestyle.

But then again, we still seem to keep our differences, even for some of these advances, for example hoover, fridge and telly, which are far more prevalent in the UK than in the US. And that that sign in question - "Wait here till the red light shows" - seems to be uniquely British.

According to that Ngram, 'no-show' started to take off in Britain in about 1970, which means it's been around here all of my working life, and about the same time as quite a lot of words that originated in hippie or black American culture around the same period, such as 'hype', 'uptight', 'the munchies', 'laid back' etc, which I wouldn't now regard as particularly American, although their origins undoubtedly are.

And like those other words, its use is now deeply embedded in the British media, so again, despite its origins, I don't really think of it as American. But then again, I spent much of the late sixties and early seventies reading Rolling Stone and American books.

I imagine that what mainly accounts for the difference in usage between AmE and BrE is its use in the former as an adjective, which seems to dominate at Google Books, whereas as far as I know its use in Britain is restricted to it being a noun. The earliest examples at Google Books are of adjectival use, from 1957 and 1958, noun use from 1965 (funnily enough, referring to students).

@jayles - incidentally, while I agree that 'show' to mean 'show up' is mainly American English (and is shown as such in, for example, the Oxford Advanced Learner's Dictionary), I don't think that there is such a distinction with 'a no-show'.

Unlike the former, OALD lists it without any mention of it being American; in Ngram its use is almost exactly the same in American and British books, and I certainly use it myself when no students turn up for a class (not such an infrequent occurrence when you teach in-company).

Strangely, it seems to be used more in the British media than in some of their American counterparts: The Guardian gets 119 hits whereas The New York Times gets none, although there seem to be plenty at the Washington Post (176) and the LA Times (125); The Daily Mail gets 437, but at the tabloid NY Post it's zilch; at the BBC there are 91, while ABC, NBC and CBS together can only muster 9. As it is seen as informal, it is perhaps not surprising that it crops up a bit more on Fox News - 152 hits.

These site searches don't seem to be 100% accurate, however, as I've found an example at the NY Post - "Super Mario ‘granny groper’ a no-show in court", and being used as an adjective at the NY Times - "No-Show Jobs and Overstaffing Hurt New York Harbor, a Report Says".

Other examples of adjectival use:
"How Restaurants Can Deal With No-Show Diners" - Eater.com
"Hotel's no-show charge" - TripAdvisor
"A $15.00 per player no-show fee will be charged" - NY State Parks

@jayles - It's a standard road sign in the UK, approved by the Department of Transport, and often used at road works - http://www.google.com/search?q=%22when+red+light+shows%22&source=lnms&tbm=isch&sa=X&ei=2gAmVKDAG4fPaJT8gNAM&ved=0CAkQ_AUoAg&biw=1018&bih=616&gws_rd=ssl

The UK press had some fun when a pedestrian stopped at one earlier this year - http://metro.co.uk/2014/01/18/coventry-pedestrian-snapped-waiting-at-red-light-intended-for-traffic-4267836/

And it's not particularly new:

"The rain poured down, and never a light showed" - Mark Twain, Huckleberry Finn, 1899

"Close to the top of the staircase, however, there opened a door, through which a warm light was showing" - Margaret Oliphant, 1884

"and at night the light shows plain enough to warn vessels that it is time to haul offshore" - US Lighthouse Board 1852

"The fact, however, is that nearly every merchant vessel's side lights show not from right ahead only, but from half a point to a whole point or more across the bow." - The Practical Mechanics Journal 1868

@Skeeter Lewis - what's wrong with intransitive 'show'?

From various dictionaries:

Fear showed in his eyes.
She tried not to let her disappointment show.
She's nearly forty now.And it shows.
They managed to fix it so that the break wouldn't show.
Her scar doesn't show, because her hair covers it.
Shirl was four months gone and just starting to show.
Now showing at a cinema near you!