For each of the following, use the truth-functional form algorithm to annotate t

Question

For each of the following, use the truth-functional form algorithm to annotate the sentence and determine its form. Then classify the sentence as (a) a tautology, (b) a logical truth but not a tautology, or (c) not a logical truth. (If your answer is (a), feel free to use the Taut Con routine in Fitch to check your answer.)

1. x x = x 2. x Cube(x) Cube(a) 3. Cube(a) x Cube(x) 4. x (Cube(x) Small(x)) x (Small(x) Cube(x)) 5. v (Cube(v) Small(v)) ¬¬v (Cube(v) Small(v)) 6. x Cube(x) ¬x ¬Cube(x) 7. [z (Cube(z) Large(z)) Cube(b)] Large(b) 8. x Cube(x) (x Cube(x) y Dodec(y)) 9. (x Cube(x) y Dodec(y)) x Cube(x) 10. [(u Cube(u) u Small(u)) ¬u Small(u)] ¬u Cube(u)

Explanation / Answer

(According to Chegg policy, only four subquestions will be answered. Please post the remaining in another question)

5. v (v3 Small(v)) ~~v (v3 Small(v))

As ~~a = a, the statement is equivalent to

v (v3 Small(v)) v (v3 Small(v))

which is the same statement twice.

So this is a tautology.

6. x x3 ~x ~x3

The satement ~x ~x3 is equivalent to x x3

Thus the statement is a tautology.

7. [z z3 Large(z)) b3] Large(b)

Since z z3 Large(z)), b3 -> Large(b)

Thus it is a tautology.

8. x x3 (x x3 y Dodec(y))

The -> operator returns false only when the left hand side of it is true and right hand side is false

If x x3 is true then x x3 y Dodec(y) is true since the v operator is true even if one of the operands is true.

Therefore the statement is a tautology.

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.