I just really need the answers, work in not required

uestion 1 Select the law which shows that the two propositions are logically equivalent. rA(pvq) rA(qvp) O Associative law O Distributive law O DeMorgan's law O Commutative lawSelect the set that corresponds to the relation given in the arrow diagram below. Rows of the matrix are numbered 1 through 4 from top to bottom and columns are numbered 1 through 4 from left to right. O 1 0 0 0 1 0 0 0 1 0 0 0 0 0 Of (1, 2), (2, 2), (2, 4), (3, 3) } Of (2, 1), (2, 2), (3, 3), (4, 2) } Of (1, 2), (2, 3), (2, 4), (3, 3) } Of (2, 1), (2, 2), (3, 3), (3, 4) }Select the set that is equal to: 3, 5, 7, 9, 11, 13 O (xEZ:3y) What is T.S O OS OT O RxR (all pairs of real numbers)Select the pair of vertices such that there is no walk of length 4 in G from the first vertex to the second vertex. 3 2 4 O 1, 3 O 2, 1 0 4, 3 O 1, 4Theorem: If r and s are rational numbers, then the product of r and s is a rational number. Which facts are assumed in a direct proof of the theorem? Or = a/b, and s = c/d, where a, b, c, d are integers. Or = a/b, and s = c/d, where a, b, c, d are integers. Ors = a/b, where a and b are integers. rs = a/b, where a and b are integers.Select the statement that is not a proposition. O Chocolate is the best flavor. Take out the trash. 5+4 =8 O It will be sunny tomorrow.\fTheorem: For any two real numbers, x and y, if x and y are both rational then x + y is also rational. Which facts are assumed and which facts are proven in a proof by contrapositive of the theorem? O Assumed: x is rational or y is rational Proven: x + y is rational O Assumed: x is rational and y is rational Proven: x + y is rational Assumed: x + y is irrational Proven: x is irrational and y is irrational Assumed: x + y is irrational Proven: x is irrational or y is irrationalQuestion 3 The domain of a relation is the set of real numbers. is related to under relation if R . Select the description that accurately describes relation R ONeither reflexive nor anti-reflexive O Transitive O Anti-reflexive O ReflexiveQuestion 4 The predicate T is defined as: T(x,y,z):(x+y)^2=z Select the proposition that is true. O T(4, 1, 5) O T(4, 1, 25) O T(1, 1, 1) O T(4, 0 2)[Quench 5 Start with the number n = 32844. Divide n by 7 end mund the result down to an integer. Keep repeating the division and rounding step until the resulting number is less then 7. How many divisions are perfumed? 0 \"097323441 0 L|09732344l 0 r32344m o L32344n J Question 6 The propositional variables f, h, and p represent the propositions: f: The student got an A on the final. h: The student turned in all the homework. p: The student is on academic probation Select the logical expression that represents the statement: "The student is not on academic probation and the student got an A on the final or turned in all the homework." O -PA(fvh) O -PAfAh O -(pAfjvh O (-pAfjuhQuestion 7 Select the set that is equivalent to (BNCjue . O BNC Oe OC OBA = {a, b, c, d} X = {1, 2, 3, 4) The function f:A-X is defined by the arrow diagram below. Select the set of pairs that defines a function that is equal to f. a - b 2 C 3 d 4 Of = {(a, 1), (b, 3), (c, 4), (d, 4)} Of = {(a, 2), (b, 3), (c, 4), (d, 4)} Of = {(a, 2), (b, 3), (d, 2)} Of = {(a, 2), (b, 3), (c, 4), (d, 2)}Select the relation that is an equivalence relation. The domain is the set (1, 2, 3, 4). O { (1, 4), (4, 1), (1, 3), (3, 1), (2, 2) } O { (1, 4), (4, 1), (1, 1), (2, 2), (3, 3), (4, 4) } O { (1, 4), (4, 1), (2, 2), (3, 3) } O { (1, 4), (4, 1), (1, 3), (3, 1), (1, 1). (2, 2), (3, 3), (4, 4) }