DISCRETE MATH, PLEASE ANSWER ALL QUESTIONS CLEARLY. - THANKYOU Suppose you wish
ID: 3195449 • Letter: D
Question
DISCRETE MATH, PLEASE ANSWER ALL QUESTIONS CLEARLY. - THANKYOU
Suppose you wish to prove P Q using the contrapositive method. The structure of the proof would be (A) Suppose P and deduce Q (B) SupposeP and deduceQ (C) Suppose~Q and deduce~P (D) SupposeP and~Q 2. Suppose you are trying to prove the following Proposition by using direct proof: 3 mod 4, then n is Proposition 1 : If n is a positive integer such that n 2 mod 4 or n not a perfect square. Which of the followings should be the first sentence of your proof (A) Suppose n is a positive integer such that n 2 mod 4 or n-3 mod 4 (B) Suppose n is a positive integer such that n-2 mod 4 and n 3 mod 4 (C) Suppose n is not a perfect square (D) Suppose n is a perfect square 3. Suppose you are trying to prove the following Proposition by using contrapositive proof Proposition 1 : If n is a positive integer such that n : 2 mod 4 or n = 3 mod 4, then n is not a perfect square. Which of the followings should be the first sentence of your proof (A) Suppose n is a positive integer such that n 2 mod 4 or n 3 mod 4 (B) Suppose n is a positive integer such that n-2 mod 4 and n 3 mod 4 (C) Suppose n is not a perfect square (D) Suppose n is a perfect square 4. Definition: A real valued function f(x) is called one-to-one if z, z2 for any real numbers and x2, then f(x)f(x2) Suppose you are trying to prove that f(x) = 2.3 + 1 is one-to-one by using contrapositive proof Which of the followings should be the first sentence of your proof? (A) Assume zi 2 (B) Assume i T2 (C) Assume f(a)f(x2) for some x1,x2 (D) Assume f(zi) = f(x2) for some zi,22Explanation / Answer
1) Option C
In contrapositive, you prove PQ by assuming ¬Q and reasoning until you obtain ¬P.
2) Option A
Suppose you need to show "If P is true, then Q is true".
In a direct proof, you assume that P is true, then use inference rules and other facts to prove that Q is true.
3) Option D
In contrapositive, you prove PQ by assuming ¬Q and reasoning until you obtain ¬P.
4) option D
In contrapositive, you prove PQ by assuming ¬Q and reasoning until you obtain ¬P.
5) option B
In contrapositive, you prove PQ by assuming ¬Q and reasoning until you obtain ¬P.
i.e in last line you will prove that x1 = x2
6) Option B
because you know the final result. Just start by negating it .
7) option A
the equation is present in first part of premise, so start working on it .
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