In Example 4, what is the significant difference between the statements ~ (p → d) and ~p →~d?
EXAMPLE 4 Connecting Ideas Using If . . . Then
Suppose that p represents “The Phillies win the World Series” and k represents “Kiefer will win an Emmy.”
a) We would read the statement p → k as “If the Phillies win the World Series, then Kiefer will win an Emmy.”
b) We would write the statement “If the Phillies do not win the World Series, then Kiefer will not win an Emmy” symbolically as ~p → ~k.
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