discrete math: Prove or disprove ¬ ( p ∧ ( q ∨ r) )  ⟷ ( p ⟶ ¬q ) ∧ ( p ⟶ ¬r ) using truth table

Q: e) What is the equivalence of ((P Q) ^( Q – P))) → ( Q → P)? O(PAQ)A(¬PA¬Q))- (P-Q) O(PAQ)A(-PA¬Q)-…

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Q: construct a truth table for each statement  [p ∧ (q ∧ r)] ⇐⇒ [(p ∧ q) ∧ r]

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Q: 6. Show the validity of the logical equivalence: (p>q) =¬p+q

A: We have to solve given problem:

Q: Prove p and ¬(¬p or q) º p and ¬q without using a truth table. Show all steps. State the laws you…

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Q: ing Equivalence Laws, show that - a) ¬(¬p ∧ q) ∧ (p ∨ q) is logically equivalent to p. b) ¬(p ∨ ¬( p…

A: Given, a ¬¬p∧q∧p∨q is to be shown logically equivalent to p.b¬p∨¬p∧q is to be shown logically…

Q: (a) p q = ¬pVq (b) p⇒ g =¬g —¬p)

A: (a). In this problem to show that p→q≡¬pvq  Show draw the truth table as follows   p q p→q ~p…

Q: Use laws and logical equivalences of propositional logic to show that ¬(p ∨ ¬(p ∧ q)) is a…

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Q: Prove p Ù ¬(¬p or q) = p and ¬q without using a truth table. Show all steps. State the laws you use.

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Q: First, complete the truth-table for (R & ((P → ¬R) & (¬P → ¬R))): Does this row correspond to a P R…

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Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.