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. ' For example, the converse of 'If a thing is a dog then it is a mammal' is 'If a thing is a mammal then it is a dog.' The converse of a theorem is a theorem if and only if and are equivalent, i.e. Note that the converse of a statement is not true just because the original statement is true. Given the statement 'if, then ,' or, the converse is 'if, then. Given the statement 'if, then ,' or, the converse is 'if, then. If a conditional statement is \(p\rightarrow q\) (if \(p\), then \(q\)), then the converse is \(q\rightarrow p\) (if \(q\), then \(p\). A vertex is a point where two or more curves, lines, or edges meet in the case of a triangle, the three vertices are joined by three line segments called edges. 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). A triangle is a polygon that has three vertices. 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. The contrapositive is logically equivalent to the original statement. If the “if-then” statement is true, then the contrapositive is also true.
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