the given logical expression
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Discrete Structures Practice Problem: Negated and Nested Quantifiers
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- Determine whether the following is true or false. Please cite the brief explanation so that I can know why is it true or false. A) 1 ∈ {{1},{2},{3}} B) A\B = A ∩ B^c C) The contrapositive of p -> (p V ¬p) = (¬p∧ q) -> ¬pGiven the universal set of nonzero INTEGERS, determine the truth value of the following statement.1. Which of the following statements are true? (a) |N|=|Z| (b) |N|<|Z| (c) |Z|=א0 (d) |R|>|Z| 2. Which of the following statements are tautologies? (a) P → Q (b) P ∧ ¬P (c) P ∨ ¬P (d) P → P 3. The contrapositive equivalency of ¬Q → P is given by: (a) P → Q (b) Q → P (c) ¬P → Q (d) ¬Q→P
- Given the following definitions: U={a,b,c, d, e, f, g} A={a, c, e, g} B={a,b,c,d} find A n BLet A = {c, n, b}, B = {x, y} and C = {0, 1}. Find A)A X B X C B)C X B X A C)B X C X CDetermine the truth value of each of the following statements. We assume that the domain for all variables consists of all integers. 1. n m (n2< m)2. n m (n < m2)3. n m (n + m = 0)4. n m (nm = m)5. n m (n2+ m2= 5)6. n m (n2+ m2= 6)7. n m (n + m = 4 n – m =1)8. n m (n + m = 4 n – m =2)9. n m p (p = (m + n)/2)
- Consider the following function someFunc::Integer -> Integer -> Integer -> Integer someFunc x y z = x *(y + z) Prove that someFunc a b c = sumFunc a c bLet A = {a, b, c}, B = {x, y}, and C = {0, 1}.Let S = {x | x = 3n, n ∈ Z+}. Which of the following expression(s) is/are true?a. 3 ∈ S b. 3 + 6 ∈ S c. ∅ ⊂ S d. S ⊆ S e. 1 ∈ S
- Given the codes and . Consider the following statements: (1) The minimum distance of a code is the smallest distance between all pairs of codewords in a code. (2) The minimum distance of code C is less than the minimum distance of code D. Group of answer choices A. Both statements are FALSE. B. Both statements are TRUE. C. Only statement (1) is TRUE. D. Only statement (2) is TRUE.Suppose that you are given the following logical statement:¬ P ∧ Q → ¬ R ∨ SBased on our discussion of order of operations, which is the correct way to interpretthis?(a) ¬(P ∧ ((Q → (¬R)) ∨ S))(b) (¬(P ∧ (Q → (¬R)))) ∨ S(c) ((¬P) ∧ (Q → (¬R))) ∨ S(d) (¬P) ∧ ((Q → (¬R)) ∨ S)(e) (¬(P ∧ Q)) → (¬(R ∨ S))(f) ((¬P) ∧ Q) → ((¬R) ∨ S)(g) ((¬P) ∧ (Q → (¬R))) ∨ S(h) ((¬P) ∧ (Q → (¬R))) ∨ S(i) (¬P) ∧ ((Q → (¬R)) ∨ S)(j) ¬((P ∧ Q) → (¬(R ∨ S)))Determine if the following argument is valid or invalid. State if valid or invalid and the the law or fallacy used to support your answer. [((p ∧ q) → ¬r) ∧ r] → ¬(p ∧ q)