A. Use truth tables to
verify these equivalences
1. p∨p ≡ p
2. p∧p ≡ p
3. p∨(p∧q) ≡ p
4. p∨q ≡¬p → q
5. p∧q ≡¬(p →¬q)
6. p ↔ q ≡ (p → q)∧(q
→ p)
B.
Determine the truth value of each of these statements. (Assume the
domain of variables consist of all real numbers).
1. ∃x(x2 = 2)
2. ∃x(x + 2 = x)
3. ∀x(x2 + 2 >
0)
4. ∀x(x2 = x)
Prove that (((p v ~q) ⊕ p) v ~p) ⊕ (p v ~q) ⊕ (p ⊕ q) is
equivalent to p ^ q. Please show your work and name all the logical
equivalence laws for each step. ( v = or, ~ = not, ⊕ = XOR)
Thank you
Using logical equivalence laws, show that (((p v ~ q) ⊕ p) v ~p)
⊕ (p v ~q) is equivalent to p v q. v = or, ~ = not, ⊕ = exclusive
or (XOR). Please show the steps with the name of the law beside
each step, thanks so much!