Advanced Reasoning & Mixed Problems

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Try the first 5 questions

1.
The statement (p -> q) AND (p -> not q) is logically equivalent to:
2.
Use strong induction to prove every integer n >= 2 is a product of primes. In the inductive step for composite k+1, we write k+1 = a * b where:
3.
Prove by induction: For all n >= 1, 1/(1*2) + 1/(2*3) + ... + 1/(n(n+1)) = n/(n+1). The inductive step gives:
4.
The number of tautologies among all truth functions of 2 variables is:
5.
The statement (p -> q) -> (not q -> not p) is:

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