Question

Check all the statements that are true:

a. A predicate is a proposition-valued function.
b. It is possible to define disjunction using only negations and conjunction.
c. A conditional is false when both premise and conclusion are false.
d. Domain-restricted universal quantification is logically equivalent to the unrestricted universal quantification of a conditional.
e. The negation of a conjunction is the disjunction of the negations.
f. Inverse and converse are logically equivalent.
g. (p→q)∧(p→¬q) is a contradiction.
h. (p→q)∨(p→¬q) is a tautology.
i. Domain-restricted existential quantification is logically equivalent to the unrestricted existential quantification of a conditional.
j. The contrapositive is the inverse of the converse.

Answer 1

true

false

true

true

false

true

false

true

true

true

Answer 2

a. True

b. False

c. True

d. True

e. False

f. True

g. False

h. True

i. True

j. True

Explanation:

The statement a and i are true. The predicates can be defined without an input variable. These numerical variables can be defined without an input variable. The statement b is false since the p to q is not in conjunction rather its contradiction.