Which of the following is contingency? (1) P ∨∼p (2) p ∧q ⇒p ∨q (3) p ∧(∼q) (4) None of these

Name: Problem 11, Chapter 5: The IIT Foundation series of Mathematics Class
Uploaded: 2021-06-18T07:10:25-08:00
Duration: 2 min 9 s
Channel: Abhijith V
Description: Which of the following is contingency? (1) P ∨∼p (2) p ∧q ⇒p ∨q (3) p ∧(∼q) (4) None of these

step 1 So here we are given four statements that is p or not p then p and q if p and q then p and not q

Which of the following is contingency? (1) P ∨∼p (2) p ∧q ⇒p...

Which of the following is contingency?
(1) $\mathrm{P} \vee \sim \mathrm{p}$
(2) $\mathrm{p} \wedge \mathrm{q} \Rightarrow \mathrm{p} \vee \mathrm{q}$
(3) $\mathrm{p} \wedge(\sim \mathrm{q})$
(4) None of these

Key Concepts

Propositional Logic

Propositional logic is the branch of logic that studies ways of joining and/or modifying entire propositions, statements, or sentences to form more complex propositions. Logical connectives such as AND, OR, NOT, and IMPLIES are used to create compound statements whose truth values can be systematically analyzed.

Implication

Implication is a logical connective that relates two propositions, typically expressed as 'if p then q' or 'p implies q'. It is fundamental to reasoning in propositional logic because it helps form complex logical structures and determines conditional relationships between statements.

Contingency

Contingency refers to a proposition in propositional logic that is neither always true (a tautology) nor always false (a contradiction). Its truth value depends on the specific assignments of truth values to its component statements, so it can be true in some cases and false in others.

Tautology

A tautology is a formula that is universally true, no matter what truth values are assigned to its constituent propositions. This means that in every possible evaluation, the proposition holds, serving as a fundamental concept in logic for determining validity.

Contradiction

A contradiction is a compound proposition that is false under every possible assignment of truth values. It represents an inconsistency within the logic, where no interpretation can ever yield a true outcome.

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