Question: ~(p?q)?(~ p?q) ? ~p Prove using Logical Equivalences using laws. Theorem 2.1.1 Logical Equivalences Given any statement variables p, q, and r, a tautology t

~(p?q)?(~ p?q) ? ~p

Prove using Logical Equivalences using laws.

Theorem 2.1.1 Logical Equivalences Given any statement variables p, q, and r, a tautology t and a con hold. 1. Commutativeiaws: pAQEqu 2. Associative laws: (p A q) A r E p A (q A r) 3. Distributive laws: p A (q v r) E (p A q) v (p A r) 4. Identity laws: p A t E p 5. Negation laws: p v ~p E t 6. Double negative law: ~(~p) E p 7. Idempotent laws: p A p E p 8. Universal bound laws: p v t E t 9. De Morgan's laws: ~(p A q) a p v ~q 10. Absorption laws: p v (p A q) E p l 1. Negations of t and c: ~t E

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

a logical equivalence is derived from Theo- rem 2.1.1. Supply a reason for each step. Theorem 2.1.1 Logical Equivalences Given any statement variables p, q, and r, a tautology t and a contradiction...

Theorem 2 . 1 . 1 Logical Equivalences Given any statement variables p , q , and r , a tautology t and a contradiction c , the following logical equivalences hold. Commutative laws: Assaciative lavs:...

Theorem 2.1.1 Logical Equivalences Given any statement variables p, q, and , a tautology t and a contradiction c, the following logical equivalences hold 1. Commutative laws 2. Associative laws: 3....

10.) (4 pts) Use Theorem 2.1.1 (not a truth table) to verify the logical equivalence: (p^(-(~p va))) v (p^) = p. 11.) (4 pts) Construct a truth table for the statement form ( pr) (q + r). Theorem...

Theorem 2.1.1 Let p, q, and r be statement variables, t al tautology, and c a contradiction. The following logical equivalences are true. 1. Commutativity: p1q=q1p; p V q =qVP 2. Associativity: (p...

In the following two problems, a set of premises and a conclusion are given. Use the valid argument forms listed in Table 2 . 3 . 1 to deduce the conclusion from the premises, giving a reason for...

Use Theorem 2.1.1 to verify the logical equivalences Supply a reason for each step Theorem 2.1.1 Logical Equivalences Given any statement variables p, q, and r, a tautology t and a contradiction c,...

Hey guy I'm currently stock with this homework for my Csc class. Can you please help me to solved it? 4. Construct the truth table for the compound proposition pq 7p (To create a table in Google...

Question 1 Given statement variables p, q, and r, a tautology t and a contradiction c, prove the Standard Logical Equivalences highlighted in blue in the following table. pVq3qvp (p V) Vr = p V (qVr)...

Explain the Securities and Exchange Commissions rationale to charge Cardillo executives with each of the following violations: a. making false representations to outside auditors b. failing to...

1. A runner makes one lap around a 200 m track in a time of 25s. What was the runner's average velocity in meter per second? . . 4 C. 0 D. 2

What is the difference between net working capital and cash?

Financial Statement Reporting for a Finance Lease Reynolds Construction (RC) needs a piece of equipment that costs $120,000. The equipment has an economic life of 3 years and no residual value. The...