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 \(q\)”). calculator will do the rest A B C Status: Calculator waiting for input. If m is an odd number, then it is a prime number. If m is not an odd number, then it is not a prime number. If m is a prime number, then it is an odd number. Suppose m is a fixed but unspecified whole number that is greater than 2. When the original statement and converse are both true then the statement is a biconditional statement. org/math/geometry/parallel-and-perpendicular-lines/triangproptut/v/proof. 1: Related Conditionals are not All Equivalent. The converse and inverse may or may not be true. The contrapositive is logically equivalent to the original statement. (iii) All sharks have a boneless skeleton. (ii) A number is divisible by 9 is also divisible by 3. (i) Two points are collinear if they lie on the same line. If the “if-then” statement is true, then the contrapositive is also true. Rewrite the following conditional statements in if-then form.
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