Question

assume the first two statements are true. is the final statement: 1) true, 2) false, or 3) uncertain based on the information provided?

all supporters of the new mayoral candidate voted in the election.
victoria did not vote in the election.
victoria was a supporter of the new mayoral candidate.

• true
• false
• uncertain

Explanation:

Analyze the first premise

Using the Logical Deduction knowledge point
The first statement is: "All supporters of the new mayoral candidate voted in the election."
This can be written as a conditional logical implication:
If a person is a supporter (\(S\)), then they voted (\(V\)).

$$S \implies V$$

Analyze the second premise

Using the Logical Deduction knowledge point
The second statement is: "Victoria did not vote in the election."
This gives us the fact:

$$ eg V$$

Apply logical deduction

Using the Logical Deduction knowledge point
By the rule of contraposition (Modus Tollens):

$$(S \implies V) \land eg V \implies eg S$$

Therefore, Victoria was not a supporter of the new mayoral candidate.

Evaluate the final statement

Using the Logical Deduction knowledge point
The final statement is: "Victoria was a supporter of the new mayoral candidate."
Since we deduced \(
eg S\) (she was not a supporter), this statement directly contradicts our logical deduction.
Thus, the final statement is False.

Answer:

• True
• False (Correct answer)
• Uncertain