p is true, q is true, and r is false, determine whether each of the following compound statements are true or false” (a) p ∧ q (b) ∼ (q ∨ r) (c) r → (p ∧ q) (d) (p ∧ r) ∨ (p ∧ q → r)

Consider the following predicate, where the domain of x and y is the set of all integers: Q(x, y) : x - y = 3 Determine the truth values of each of the following expressions. ¡¡ x\yQ(x, y) Q(4,1) Q(7,4) VxyQ(x,y) Q(4,7) 1. True 2. False

Which statement is correct ? (a){1}∈{1,2,3} (b){1}∉{1,2,3} (c){1}⊆{1,2,3} (d){1}⊂{1,2,3}

Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?(i) {3, 4} ⊂ A                                             (ii) {3, 4} ∈ A                                            (iii) {{3, 4}} ⊂ A(iv) 1 ∈ A                                                   (v) 1 ⊂ A                                                  (vi) {1, 2, 5} ⊂ A(vii) {1, 2, 5} ∈ A                                   (viii) {1, 2, 3} ⊂ A