Questions: Suppose the following situation occurred. Ann didn't put money into a savings account each month. When summertime came, Ann was able to take a vacation. Complete the table to determine the truth of Ann's mom's statement in this situation. Use T for true and F for false. You may add more columns, but those added columns will not be graded.

Solution Steps

• Let \( p \) represent "Ann put money into a savings account each month."
• Let \( q \) represent "Ann was able to take a vacation."

• According to the problem, Ann didn't put money into a savings account each month, so \( p \) is False (F).
• Ann was able to take a vacation, so \( q \) is True (T).

• \(\sim p\) means "not \( p \)", which is True (T) because \( p \) is False (F).
• \(\sim q\) means "not \( q \)", which is False (F) because \( q \) is True (T).
• The expression \(\sim p \rightarrow \sim q\) is a conditional statement. A conditional statement is False only when the antecedent (the part before the arrow) is True and the consequent (the part after the arrow) is False. In this case, \(\sim p\) is True and \(\sim q\) is False, so \(\sim p \rightarrow \sim q\) is False (F).

Final Answer