2.1-2.2 Conditionals, Inductive & Deductive Reasoning

A conditional statement is a logical statement that has the form 'If p, then q', where p is the hypothesis and q is the conclusion.

The converse of a conditional statement 'If p, then q' is 'If q, then p'.

The inverse of a conditional statement 'If p, then q' is 'If not p, then not q'.

The contrapositive of a conditional statement 'If p, then q' is 'If not q, then not p'.

A conditional statement is true unless the hypothesis is true and the conclusion is false.

If $$x=1$$ , then $$2x=2$$ .

If $$x=2$$ , then $$x^2=5$$ .

A biconditional statement is a statement that combines a conditional statement and its converse, written as 'p if and only if q'.

A biconditional statement is true if both the conditional and its converse are true.

Inductive reasoning involves making generalizations based on specific observations or examples.