converse of p→q
The converse of a conditional statement p→q is the statement q→p
The converse of a conditional statement p→q is the statement q→p. It is obtained by interchanging the hypothesis and the conclusion of the original conditional statement.
In other words, if the original statement is “If p, then q,” then the converse is “If q, then p.”
For example, the original statement is “If it is raining, then the ground is wet.” The converse of this statement would be “If the ground is wet, then it is raining.”
It is important to note that the converse of a conditional statement may not always be true. The truth value of the original statement does not necessarily imply the truth value of its converse. It is possible for the original statement to be true while its converse is false.
In mathematical logic, the validity of a conditional statement and its converse can be proved using deductive reasoning techniques, such as truth tables or logical equivalences.
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