![]() ![]() If a conditional statement is \(p\rightarrow q\), then the inverse is \(\sim p\rightarrow \sim q\).Ī statement is logically equivalent if the "if-then" statement and the contrapositive statement are both true.Ī premise is a starting statement that you use to make logical conclusions. Note that the converse of a statement is not true just because the original statement is true. If a conditional statement is \(p\rightarrow q\) (if \(p\), then \(q\)), then the converse is \(q\rightarrow p\) (if \(q\), then \(p\). If a conditional statement is \(p\rightarrow q\) (if \(p\) then q), then the contrapositive is \(\sim q\rightarrow \sim p\) (if not q then not p). What if you were given a conditional statement like "If I walk to school, then I will be late"? How could you rearrange and/or negate this statement to form new conditional statements?Ī statement is biconditional if the original conditional statement and the converse statement are both true.Ī conditional statement (or 'if-then' statement) is a statement with a hypothesis followed by a conclusion. In other words, if \(p\rightarrow q\) is true and \(q\rightarrow p\) is true, then \(p \leftrightarrow q\) (said “\(p\) if and only if \(q\)”). When the original statement and converse are both true then the statement is a biconditional statement. The converse and inverse may or may not be true. Learn what is converse in geometry and what is the converse of the Pythagorean theorem. The contrapositive is logically equivalent to the original statement. The example is given below to understand the midpoint theorem. The contrapositive of a statement has its antecedent and consequent inverted and flipped. The converse of the midpoint theorem states that if a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side. If the “if-then” statement is true, then the contrapositive is also true. In logic and mathematics, contraposition refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as proof by contraposition.
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