Answer:
Our conditional statement is: if a population consists of 50% men then 50% of the population must be women.
p→q
If we exchange the position of the hypothesis and the conclusion we get a converse statement: if a population consists of 50% women then 50% of the population must be men.
q→p
If both statements are true or if both statements are false then the converse is true. A conditional and its converse do not mean the same thing
If we negate both the hypothesis and the conclusion we get a inverse statement: if a population do not consist of 50% men then the population do not consist of 50% women.
∼p→∼q
The inverse is not true juest because the conditional is true. The inverse always has the same truth value as the converse.
We could also negate a converse statement, this is called a contrapositive statement: if a population do not consist of 50% women then the population do not consist of 50% men.
∼q→∼p
The contrapositive does always have the same truth value as the conditional. If the conditional is true then the contrapositive is true.
A pattern of reaoning is a true assumption if it always lead to a true conclusion. The most common patterns of reasoning are detachment and syllogism
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