what's the truth table(s) for (p=>q)≡((p∧¬q)=>F)? I think i'm getting confused with F being a proposition or a contradiction, the homework question didn't specify! Thank you

Given Proposition [(K ⊃ Y) • ~(~K ∨ Y)] • [K ∨ (~J ≡ ~I)]   Given Truth Values   Truth Table K Y J I   [ ( K ⊃ Y ) • ~ ( ~ K ∨ Y ) ] • [ K ∨ ( ~ J ≡ ~ I ) ] T T T T                                                         T T T F                                                         T T F T                                                         T T F F                                                         T F T T                                                         T F T F                                                         T F F T                                                         T F F F                                                         F T T T                                                         F T T F                                                         F T F T                                                         F T F F                                                         F F T T…

Which of the following are equivalent to:¬((∀x)(∃y)(∀z)(P(x)→(Q(y)∨R(z))))? (Select all that apply.) Group of answer choices (∃x)(¬(∃y)(∀z)(P(x)→(Q(y)∨R(z)))) (∃x)(∀y)(¬(∀z)(P(x)→(Q(y)∨R(z)))) (∃x)(∀y)(∃z)(¬(P(x)→(Q(y)∨R(z)))) (∃x)(∀y)(∃z)(P(x)∧¬(Q(y)∨R(z))))

This is a practice question from my Data Structures course: h(n) = {1 if n = 1; 3 × h(n - 1) - 1 otherwise} Rewrite h(n) using an explicit formula that is not recursive (i.e., succinctly express h(n) as a polynomial/exponential function of n). Also, prove the correctness of your expression using mathematical induction. Please explain how to do this (as opposed to simply providing the answer). Thank you for your assistance.