Complete each of the following problems. Be sure to include any relevant work and explanation

1. Determine whether the given logical equivalence holds and prove your claim.

a.

b.

2. Define 3 propositional variables and represent the following statement in terms of those variables. (Hint: "if" and "only if" do not generally mean the same thing). Please do not include any negation words (e.g. "not") in the defined propositions.

"The heist will succeed only if the vault has been opened and the alarm hasn't been triggered."

Hed= (1+b) (brd) 4 (IL V(be Ad))^(1vbv d) = 1+(bv )