The operators ∧ and ∨ are idempotent (see Figure 3.12)—that is, p ∧ p ≡ p ∨ p ≡ p. But ⇒, ⊕, and ⇔ are not idempotent. Simplify—that is, give as-simple-as-possible propositions that are logically...

The operators ∧ and ∨ are idempotent (see Figure 3.12)—that is, p ∧ p ≡ p ∨ p ≡ p. But ⇒, ⊕, and ⇔ are not idempotent. Simplify—that is, give as-simple-as-possible propositions that are logically equivalent to—the following

1.p ⇒ p

2. p ⊕ p

3. p ⇔ p