Question

Let p and q are two statements then "if p then q" is a compound statement, denoted by p→ q and referred as a conditional statement, or implication. The implication p→ q is false only when p is true, and q is false; otherwise, it is always true. In this implication, p is called the hypothesis (or antecedent) and q is called the conclusion

Answer 1

Conditionals in mathematics are 'if-then' statements signified by p→q. They are false only when the antecedent p is true and the consequent q is false. They involve necessary and sufficient conditions, which are key in forming logical statements and valid deductive arguments.

Step-by-step explanation:

Conditionals are a crucial part of logical reasoning in mathematics, often taking the form of 'if-then' statements. When we express a conditional as 'if p then q,' we denote it as p→ q, which means that if hypothesis p (the antecedent) is true, then q (the consequent) will also be true.

This implication is considered false only when p is true and q is false. Necessary and sufficient conditions play a key role in understanding these conditionals: a necessary condition must be present for the proposition to be true, whereas a sufficient condition guarantees the truth of the proposition. Logical statements and inferences such as modus ponens and modus tollens are used to form valid deductive arguments, making use of these principles.