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# Tag Info

## Hot answers tagged logic

33 votes

### Children's counting problems: Is this question phrased correctly?

I don't think there's anything wrong with the wording; it's clear what is being asked. Your example with the three dollars is also not always the way we speak in everyday language. If you ask someone ...
• 1,527
32 votes

• 21.7k
10 votes

### How can I teach intuition why ‘If P then Q’ and ‘P only if Q’ mean the same, to first year undergraduates?

To avoid confusion, in examples of implication, it may help to avoid any suggestion of causality, and to have both antecedent and consequent expressed in the present tense. EXAMPLE Consider the ...
• 1,186
10 votes

### Dominance of connectives: Why do we teach this?

When I see exercises like this, I often find that it teaches students to make assumptions about symbolic statements that may not be there - in a real world situation, if a statement is ambiguous, I ...
• 101
9 votes
Accepted

### Why are proofs by contradiction counterintuitive?

One reason why proof by contradiction is difficult for students is because mathematical notation (and other written language) does not allow for a subjunctive mood. Let me elaborate on this: In ...
• 17.4k
9 votes

### Is it a good idea to have one or two or three classes on basic logic before teaching $\varepsilon$-$\delta$ in Calculus?

I had the same thought this year. My suspicion was that many students get anxious about suddenly dealing with quantifiers and they also struggle with understanding how the ordering of them can affect ...
9 votes

### I want a "true" proof by contradiction of an implication $P \Rightarrow Q$

I think you are overlooking the fact that proof by contradiction must invoke the tautology $(P\ \hbox{or}\ \neg P)$, called the law of excluded middle. To prove $P\Rightarrow Q$ by contradiction, we ...
• 11k
9 votes

### How to explain (FALSE => TRUE) is TRUE

I use the example If your flight is on time, then I will pick you up from the airport. If your friend tells you this, the only time they have lied is if the premise is true and the conclusion false. ...
• 3,890
8 votes

### Children's counting problems: Is this question phrased correctly?

I showed this question to my three-year old son. His response - because he counted the apples one by one in each picture, passing "4" each time - was B, C and D. Hence, we need to take into ...
• 81
8 votes
Accepted

### Dominance of connectives: Why do we teach this?

This shouldn't be taught, and those exercises are pointless. There is clearly no intrinsic value in introducing and memorizing precedence of operations. If there is a point, it either is that we would ...
• 966
7 votes

### Is it a good idea to have one or two or three classes on basic logic before teaching $\varepsilon$-$\delta$ in Calculus?

Generally speaking, it would be nice to have a foundations class at the initiation of the Math major. Some of my colleagues envision this course centered around teaching college algebra. Well, to be ...
• 10.8k
7 votes
Accepted

### Teaching logic through "high school algebra"?

Obviously, one place to look is in the huge amount of “new math” curriculum material that was written during the late 1950s to early 1970s, but I’ll leave that for you or someone else to search ...
• 5,838
7 votes
Accepted

### "Always/Sometimes/Never" vs. "True/False" questions for mathematical reasoning

With extensive anecdotal experience, by now I scrupulously avoid such questions (and analogous ones that exactly hit at the incompatibilities between "ordinary" language and mathematical language), at ...
• 14.7k
6 votes

I would not recommend to teach this method since there are some downsides. Take $A(x) \iff x \text{ is divisible by } 2$ $B(x) \iff x \text{ is divisible by } 42$ Is $A(x) \implies B(x)$ or $B(x) \... • 2,031 6 votes ### Determining sets to show sufficiency of a condition? First, although you talk a bunch about cardinality, I don't see how that makes sense, so I'm going to assume you mean that you have them determine if the set corresponding to p is a subset of the set ... • 11.6k 6 votes ### Is it a good idea to have one or two or three classes on basic logic before teaching$\varepsilon$-$\delta$in Calculus? It is well known that learning epsilon-delta definitions is difficult and is the intellectual equivalent of jumping over a tall wall in order to join the enlighted ones on the other side, a feat never ... • 2,240 6 votes ### Is it a good idea to have one or two or three classes on basic logic before teaching$\varepsilon$-$\delta\$ in Calculus?

No. This is the same kind of pedagogical fallacy that led to the "new math" of the 1960s, when they tried to teach elementary school students deep concepts of abstract algebra as an introduction to ...
• 799
6 votes

### Book request: teaching proving and reasoning at an American university

Some things we're currently considering for a similar course at a large urban community college: Epp, Discrete Mathematics with Applications Artin, Algebra Gilbert, Elements of Modern Algebra Lay, ...
• 26.1k
6 votes

### Book request: teaching proving and reasoning at an American university

Another free option is Lehman, Leighton, and Meyer's Mathematics for Computer Science. It's written for an MIT introductory discrete math course that emphasizes training students in proof-writing.
• 161

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