Consider the following statements: S1:Every unsatisfiable is contingency S2:Every valid
Consider the following statements:
S1:Every unsatisfiable is a contingency
S2:Every valid is a contingency
S3:Every invalid is a contradiction
Which of the following options represent the correct statements?
- A.
S1 and S3
- B.
S2 and S3
- C.
S1 only
- D.
None of these
Attempted by 58 students.
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Correct answer: D
Let's analyze each statement:
S1: Every unsatisfiable is a contingency.
An unsatisfiable statement is false under all truth assignments. A contingency is true under some assignments and false under others. Since an unsatisfiable statement is never true, it cannot be a contingency. Thus, S1 is false.
S2: Every valid is a contingency.
A valid statement (tautology) is true under all truth assignments. A contingency must be true under some and false under others. Since a valid statement is never false, it cannot be a contingency. Thus, S2 is false.
S3: Every invalid is a contradiction.
An invalid statement is not true under all assignments. This includes both contradictions (always false) and contingencies (sometimes true, sometimes false). Since invalid statements can be contingencies, S3 is false.
Since all three statements are false, the correct option is 'None of these'.