What do you understand by tautology show that P ∧ Q → P ∨ Q is a tautology?

What do you understand by tautology show that P ∧ Q → P ∨ Q is a tautology?

To show (p ∧ q) → (p ∨ q). If (p ∧ q) is true, then both p and q are true, so (p ∨ q) is true, and T→T is true. If (p ∧ q) is false, then (p ∧ q) → (p ∨ q) is true, because false implies anything.

What is logically equivalent to Q → P?

Logical Equivalence. Two (molecular) statements P and Q are logically equivalent provided P is true precisely when Q is true. That is, P and Q have the same truth value under any assignment of truth values to their atomic parts.

How do you solve logically equivalent?

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. Beside distributive and De Morgan’s laws, remember these two equivalences as well; they are very helpful when dealing with implications. p⇒q≡¯q⇒¯pandp⇒q≡¯p∨q.

How do you prove logically equivalent?

What is logically equivalent statements?

Two statement forms are logically equivalent if, and only if, their resulting truth tables are identical for each variation of statement variables. p q and q p have the same truth values, so they are logically equivalent.

How do you know if two statements are logically equivalent?

Two statement forms are called logically equivalent if, and only if,they have identical truth values for each possible substitution for theirstatement variables. Two statement forms are called logically equivalent if, and only if,they have identical truth values for each possible substitution for theirstatement variables.

What is the double implication of P and Q?

means that P and Q are equivalent. So the double implication is true if P and Q are both true or if P and Q are both false ; otherwise, the double implication is false. You should remember — or be able to construct — the truth tables for the logical connectives.

What is a statement form in logic?

2.1 Logical Equivalence and Truth Tables statement form (or propositional form) is an expression made up ofstatement variables (such as p,q, andr) and logical connectives (suchas ;^, and_) that becomes a statement when actual statementsare substituted for the component statement variables.

What is a truth table in math?

A truth table shows how the truth or falsity of a compound statement depends on the truth or falsity of the simple statements from which it’s constructed. So we’ll start by looking at truth tables for the five logical connectives. Here’s the table for negation: