For each of the following, use the truth-functional form algorithm to annotate t
ID: 3141060 • Letter: F
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)
1. x x = x2
x = x2 => x = 0 or x = 1
Thus the statement is not true x but only for specific values.
Hence it is a logical statement but not a tautology.
2. x x3 -> a3
This statement is not true as a need to be the example of x3.
So the statement is a logical statement but not a tautology.
3. a3 -> x x3
As for x = a, x x3 is true, the statement is a tautology.
4. x (x3 Small(x)) x (Small(x) x3)
The ^ operator is associative.
a ^ b = b ^ a
Therefore the statement is a tautology.
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