Show that ∼ p ∧ (p ∧ q) is a contradiction.
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Show that ∼ p ∧ (p ∧ q) is a contradiction.
To show that ~p∧(p∧q) is a contradiction, we must show that it is always false regardless of the true values of p and q.
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- Let R=ABCDEGHK and F= {ABK→C, A→DG, B→K, K→ADH, H→GE} . Is it in BCNF? Prove your answer.Prove or disprove that for any x ∈ N, x(x+1)/2 ∈ N (where N = {0, 1, 2, 3, ….}A) Prove that if A ⊆ B and B ⊆ C, then A ⊆ C.B) Prove that if (A − B) ∪ (B − A) = A ∪ B, then A ∩ B = ∅, using proof by contradiction.
- Suppose we have positive integers a, b, and c, such that that a and b are not relatively prime, but c is relatively prime to both a and b . Let n = s × a + t × b be some linear combination of a and b, where s and t are integers. Prove that n cannot be a divisor of c. Follow the definition of relative primes, and use contradiction.Find the value of x for the following sets of congruence using the Chinese remainder theorem.a. x ≡ 2 mod 7, and x ≡ 3 mod 9b. x ≡ 4 mod 5, and x ≡ 10 mod 11c. x ≡ 7 mod 13, and x ≡ 11 mod 12Solve this and show how you solved it Construct a truth table for the following, remembering to observe the order of operations discussed in class: q Λ ~p → r
- Prove that it is logically equal using common equivalent proposition. 1. ¬[p v (¬p ˄ q) ≡ (¬p ˄ ¬q) 2. p → (q ˄ ¬r)Show that(s∗)∗=s when s is a compound propositionUsing the method of full or partial truth tables, say whetherthe following sentences of L1 are tautologies or not. If not,give a counterexample. (a) ¬(P → Q) → (P → ¬P)