Question

Use an ordinary truth table to answer the following problems. Construct the truth table as per the instructions in the textbook.

Given the statement: (Fv~S)⊃~(Sv~F)
This statement is:
a. Contingent.
b. Self-contradictory.
c. Inconsistent.
d. Valid.
e. Tautologous.

Answer 1

The given statement is false for all possible combinations of truth values of the variables F and S.

Step-by-step explanation:

The given statement is: (Fv~S)⊃~(Sv~F)

To construct a truth table for this statement, we need to consider all possible combinations of truth values for the variables F and S.

We can start by listing all possible values of F and S:

• F = T, S = T
• F = T, S = F
• F = F, S = T
• F = F, S = F

Next, we substitute these values into the given statement and evaluate the truth value of the statement for each combination:

• (T v ~T)⊃~(T v ~T) = (T v F)⊃~(T v T) = T⊃~T = F
• (T v ~F)⊃~(F v ~T) = (T v T)⊃~(F v F) = T⊃~F = F
• (F v ~T)⊃~(T v ~F) = (F v F)⊃~(T v T) = T⊃~T = F
• (F v ~F)⊃~(F v ~F) = (F v T)⊃~(F v T) = T⊃~T = F

Based on the truth table, we can conclude that the given statement is false for all possible combinations of truth values of F and S.