What equivalence/law was applied? [(p v q) ^ (p → r) ^ (q → r)] → r = ¬[(p v q) ^ (p → r) ^ (q → r)] v r O De Morgan's law commutativity and associativity associativity and an idempotent law O conditional-disjunction equivalence

A logical equivalence is derived from Theorem 2.1.1. Supply a reason for each step.

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

Using the substitution theorem and the important equivalences (handout) show the following equivalence. Use only one substitution/equivalence rule (such as absorption) per step and justify each step by name. ((-p) → (r V q)) = ((¬r) → ((¬p) → q))

1 If R is reflexive, then R is reflexive. True False

Prove the logical statements are equivalent by converting left side to the right hand side (be sure to state equivalence use in conversion like Demorgan, Associativity and Distributive)