~q → ~p
The expression ~q → ~p is an example of a logical statement that uses conditional reasoning
The expression ~q → ~p is an example of a logical statement that uses conditional reasoning. It is read as “not q implies not p” or “if not q, then not p.”
To understand the meaning of this statement, we need to know that the symbol ~ represents negation or “not.” So, ~q means “not q” and ~p means “not p.”
The arrow symbol → is used to indicate implication or the conditional relationship between two statements. In the statement ~q → ~p, the tilde (~) is placed in front of both q and p, signifying the negation of both.
The overall statement can be interpreted as follows: If q is false, then p must also be false. It asserts that the negation of q implies the negation of p.
This logical statement can be represented using a truth table:
q | p | ~q | ~p | ~q → ~p
—————————
T | T | F | F | T
T | F | F | T | T
F | T | T | F | F
F | F | T | T | T
The truth table shows that ~q → ~p is true in three out of the four possible cases. It is only false when q is false and p is true.
In terms of everyday examples, let’s consider the statement “If it is not raining, then I will not bring an umbrella.” In this case, the statement ~q → ~p can be interpreted as “If it is not raining, then I will not bring an umbrella.” It means that if it is not raining (~q), then I will not bring an umbrella (~p).
So, in summary, the statement ~q → ~p represents a logical implication that states if one statement (q) is false, then another statement (p) must also be false.
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