In the truth table for the statement form p $\supset$ q, the column of truth values underneath the consequent should be:

Question

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The statement form p F1F1F1S1F1F1F10 q is a conditional statement, which means that the truth value of the consequent (q) is dependent on the truth value of the antecedent (p F1F1F1S1).

The antecedent has three variables: p, F1, and S1. Each of these variables can be either true (T) or false (F), which means that there are 2^3 = 8 possible combinations of truth values for the antecedent.

The consequent has two variables: F1 and F10. Each of these variables can also be either true or false, which means that there are 2^2 = 4 possible combinations of truth values for the consequent.

Therefore, the truth table will have 8 rows (one for each possible combination of truth values for the antecedent) and 4 columns (one for each possible combination of truth values for the consequent).

Since there are only 4 possible combinations of truth values for the consequent, and there are 8 rows in the truth table, some of these rows must have the same truth value for the consequent.

Looking at the given statement form, we can see that the consequent (F1F1F10 q) is true only when both F1 and F10 are true. Therefore, the truth value of the consequent will be true (T) only for the combinations of truth values for F1 and F10 that are both true.

There are two combinations of truth values for F1 and F10 that are both true: (T,T) and (F,T). Therefore, the column of truth values underneath the consequent should be TFTF (or equivalent, such as TTFT or FTTF).

The only choice that matches this column is C).

In the Truth Table for the Statement Form P ⊃\supset⊃ Q, the Column of Truth Values Underneath the Consequent Should

In the Truth Table for the Statement Form P $\supset$ Q, the Column of Truth Values Underneath the Consequent Should