Construct proofs to show that the following symbolic arguments are valid. Commas mark the breaks between premises, ‘∴’ precedes the conclusion. You may use the following rules: MP, MT, DS, HS, CD, Simp, Conj, Add (M ∨ N) → ∼S, T → (M ∨ N), ∼S → ∼(M ∨ N) ∴ T → ∼(M ∨ N)

Use a truth table to show that this logical law is a tautology: p v (q Ar) = (p v q) ^ (p V r)

Proofs: Construct proofs to show that the following symbolic arguments are valid.  Commas mark the breaks between premises, ‘∴’ precedes the conclusion. You may use any rule, but you must use CP (H∨E)→K ∴E→K

Let M(x,y) be the predicate "person x has seen movie y," where the domain for x is the set of all people and the domain for y is the set of all movies. Express the following English sentence as a symbolic proposition: "There is a movie that has not been seen by any people." x-M(x,y) ⒸyVx-M(x, y) x-M(x,y) yx M(x,y) -