Answer:
see below
Step-by-step explanation:
Like a lot of math, it is about matching patterns. The pattern of a conditional statement is ...
if <em>hypothesis</em>, then <em>conclusion</em>.
In problems 1 and 2, you are asked to identify the <em>hypothesis</em> and <em>conclusion</em> in each if ... then ... statement. The hypothesis is the clause between "if" and "then"; the conclusion is the clause following "then."
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1. <u>Hypothesis</u>: the product of two numbers is zero.
<u>Conclusion</u>: at least one of the numbers must be zero.
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2. <u>Hypothesis</u>: it is daylight saving time.
<u>Conclusion</u>: I must reset my clocks.
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3. Inverse and converse are different ways to rewrite the conditional using the same clauses (possibly negated).
Original conditional: If <em>p</em>, then <em>q</em>.
Inverse: If <em>not p</em> then <em>not q</em>.
Converse: If <em>q</em>, then <em>p</em>.
Here, you are given clauses <em>p</em> and <em>q</em>. You just need to put them into the appropriate forms.
<u>Conditional</u>: If it is St. Patrick's Day, then it is March.
<u>Inverse</u>: If it is not St. Patrick's Day, then it is not March.
<u>Converse</u>: If it is March, then it is St. Patrick's Day.
<u>Truth value</u>: The conditional is true; the inverse and converse are false.
