Question

In the following exercises: (a) use the logical equivalences p -> q ≡∼ p ∨ q and p ↔ q ≡ (∼ p ∨ q) ∧ (∼ q ∨ p) to rewrite the given statement forms without using the symbol -> or ↔, and (b) use the logical equivalence p ∨ q ≡∼ (∼ p∧ ∼ q) to rewrite each statement form using only ∧ and ∼. 1 (a) p∧ ∼ q -> r (b) p∨ ∼ q -> r ∨ q (c) (p -> r) ↔ (q -> r) (d) (p -> (q -> r)) ↔ ((p ∧ q) -> r)

Name: in the following exercises a use the logical equivalences p q p q and p q p q q p to rewrite the given statement forms without using the symbol or and b use the logical equivalence p q p q t 53673
Uploaded: 2022-03-17T09:37:40-08:00
Duration: 1 min 38 s
Channel: Rahi P
Description: in the following exercises a use the logical equivalences p q p q and p q p q q p to rewrite the given statement forms without using the symbol or and b use the logical equivalence p q p q t 53673

          In the following exercises: (a) use the logical equivalences p ->
q ≡∼ p ∨ q and p ↔ q ≡ (∼ p ∨ q) ∧ (∼ q ∨ p) to rewrite the given
statement forms without using the symbol -> or ↔, and (b)
use the logical equivalence p ∨ q ≡∼ (∼ p∧ ∼ q) to rewrite each
statement form using only ∧ and ∼.
1
(a) p∧ ∼ q -> r
(b) p∨ ∼ q -> r ∨ q
(c) (p -> r) ↔ (q -> r)
(d) (p -> (q -> r)) ↔ ((p ∧ q) -> r)

Added by Gary H.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Rahi P

03/17/2022

Step 1

Step 1: Using the logical equivalence p -> q ≡ ∼ p ∨ q, we can rewrite the statement forms without using the symbol -> as follows: (a) p∧ ∼ q -> r ≡ ∼ (p∧ ∼ q) ∨ r ≡ (∼ p ∨ q) ∨ r (b) p∨ ∼ q -> r ∨ q ≡ ∼ (p∨ ∼ q) ∨ (r ∨ q) Show more…

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In the following exercises: (a) use the logical equivalences p -> q ≡∼ p ∨ q and p ↔ q ≡ (∼ p ∨ q) ∧ (∼ q ∨ p) to rewrite the given statement forms without using the symbol -> or ↔, and (b) use the logical equivalence p ∨ q ≡∼ (∼ p∧ ∼ q) to rewrite each statement form using only ∧ and ∼. 1 (a) p∧ ∼ q -> r (b) p∨ ∼ q -> r ∨ q (c) (p -> r) ↔ (q -> r) (d) (p -> (q -> r)) ↔ ((p ∧ q) -> r)