4.For (2) to be false, q = T and u = F. We can try to find an assignment of the other variables that will make (1) true. For p ⊃ (q⊃r.(s∨t)) to be true, r = s = t = T. In this case, (-p.q.∨r.s∨r.t)⊃u becomes false, so the conjunct is false as well. Any other assignments of r, s, and t will make the first part of the conjunct false, thus making the entire conjunct false. Thus for all truth-values making (2) false, (1) is false as well, and (1) implies (2).

5.First schematize the statements.p = prices are lowq = sales are highr = you sell quality merchs = your customers are satisfied (ai){|! becomes (p || ⊃ q || r || p) .-(r || p.q || p.q ⊃ r || s); (ii) becomes (p.-∨ r ∨ ) ⊃ (p.q ⊃ r∨ s).|-|T || (ii) is false when p∨r = T || T || and q∨s = F || T || T || T|-|T || T || F || T || T || F || T|-|T || F || T || F || F || T || T|-|T || F || F || T || F || T || T|-|F || T || T || F || F || T || T|-|F || T || F || F || F || T || T|-|F || F || T || F || F || T || T|-|F || F || F || F || F || T || T|}(b){|! p || q || r || s || -p.-q || This means that q.-= s || = F and p.-!= r.s || -p.-q ∨ q.-s ∨ p.-r.and s|-| T || T || T || T || F || F || F || F|-| T || T || T || F || F || T || F || T|-| T || T || F || T || F || F || T || T|-| T || T || F || F || F || T || F || T|-| T || F || T || T || F || F || F || F|-| T || F || T || F || F || F || F || F|-| T || F || F || T || F || F || T || T|-| T || F || F || F || F || F || F || F|-| F || T || T || T || F || F || F || F|-| F || T || T || F || F || T || F || T|-| F || T || F || T || F || F || F || F|-| F || T || F || F || F || T || F || T|-| F || F || T || T || T || F || F || T|-| F || F || T || F || T || F || F || T|-| F || F || F || T || T || F || F || T|-| F || F || F || F || T || F || F || T|}being false makes (ci){|! false regardless of the values of p || q || r || (p∨q)≡-and r || p∨, so (-q ⊃ ri) || implies (p∨qii)≡-r . p∨(-q ⊃ r)|-|T || T || T || F || T || F|-|T || T || F || T || T || T|-|T || F || T || F || T || F|-|T || F || F || T || T || T|-|F || T || T || F || T || F|-|F || T || F || T || T || T|-|F || F || T || T || T || T|-|F || F || F || F || F || F|}