Consider the wff (p→q) → r. (2) (2a) Write down its contrapositive. (2b) Start with the contrapositive in (2a) and rewrite using logical equiv- alences so that the final wff involves only variables, their negations, conjunctions, and disjunctions.
Contrapositive: The contrapositive of a conditional statement is formed by negating both the hypothesis and the conclusion of the original statement, and then switching their order. For example, if the original statement is "If it is raining, then the ground is wet," then the contrapositive would be "If the ground is not wet, then it is not raining." The contrapositive is logically equivalent to the original statement, meaning that if the original statement is true, then its contrapositive must also be true.
Logical Equivalence: Two statements are said to be logically equivalent if they have the same truth value under all possible conditions. In other words, if two statements are logically equivalent, then they are either both true or both false for any given situation. For example, the statements "It is raining and the ground is wet" and "If the ground is not wet, then it is not raining" are logically equivalent, because they have the same truth value under all possible conditions. The symbol for logical equivalence is a double arrow (↔️), which is read as "if and only if."
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