How do you show that a conditional statement is it tautology without using truth tables?

How do you show that a conditional statement is it tautology without using truth tables?

Show that the conditional statement is a tautology without using…

1. [(p→q)∧(q→r)]→(p→r)
2. ¬[(p→q)∧(q→r)]∨(p→r)
3. ¬[(¬p∨q)∧(q→r)]∨(p→r)
4. [¬(¬p∨q)∧¬(q→r)]∨(p→r)
5. [(p∧¬q)∧(q∧¬r)]∨(p→r)

Which is the name of the logically equivalent P ∧ Q ∨ R ≡ P ∧ Q ∨ P ∧ R?

Since columns corresponding to p∨(q∧r) and (p∨q)∧(p∨r) match, the propositions are logically equivalent. This particular equivalence is known as the Distributive Law.

What are the laws for logical equivalences?

Some Laws of Logical Equivalence

• Idempotent Laws. (i) p ∨ p ≡ p.
• Commutative Laws. (i) p ∨ q ≡ q ∨ p.
• Associative Laws. (i) p ∨ ( q ∨ r ) ≡ ( p ∨ q ) ∨ r (ii) p ∧ ( q ∧ r ) ≡ ( p ∧ q ) ∧ r .
• Distributive Laws.
• Identity Laws.
• Complement Laws.
• Involution Law or Double Negation Law.
• 8. de Morgan’s Laws.

How do you find logically equivalent statements?

To test for logical equivalence of 2 statements, construct a truth table that includes every variable to be evaluated, and then check to see if the resulting truth values of the 2 statements are equivalent.

Which of the following is are logically equivalent to P → Q ∧ P → R )?

(p ∧ q) → r is logically equivalent to p → (q → r).

Is P → Q ∨ q → p a tautology?

Look at the following two compound propositions: p → q and q ∨ ¬p. (p → q) and (q ∨ ¬p) are logically equivalent. So (p → q) ↔ (q ∨ ¬p) is a tautology. Thus: (p → q)≡ (q ∨ ¬p).

What is the truth value of ∼ P ∨ q ∧ P?

So because we don’t have statements on either side of the “and” symbol that are both true, the statment ~p∧q is false. So ~p∧q=F. Now that we know the truth value of everything in the parintheses (~p∧q), we can join this statement with ∨p to give us the final statement (~p∧q)∨p….Truth Tables.

How do you verify logical equivalences?

Is {[( P ∧ Q → R → P → Q → R )]} tautology?

Thus, `[(p to q) ^^(q to r) ] to ( p to r)` is a tautolgy. Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

What is logical equivalence in math?

Two logical statements are logically equivalent if they always produce the same truth value. Consequently, p≡q is same as saying p⇔q is a tautology.

What is the value of p ∧ q ∨ (~ p ∨ q when p is true and q is false?

So because we don’t have statements on either side of the “and” symbol that are both true, the statment ~p∧q is false. So ~p∧q=F. Now that we know the truth value of everything in the parintheses (~p∧q), we can join this statement with ∨p to give us the final statement (~p∧q)∨p….Truth Tables.