Question

Consider the following statement

∀ integer d, if 6/d is an integer then d= 3.
Which of the following is a negation for the statement?
a. ∃ an Integer d such that 6/d is an Integer and d≠3.
b. ∃ an Integer d such that 6/d is not an Integer d=3.
c. ∀ Integer d, If 6/d is not an Integer, then d≠3.
d. ∀ Integer d, If d≠3, then 6/d is not an Integer.
e. ∀ Integer d, If d=3, then 6/d is an Integer

Answer 1

The negation of the statement is option a. ∃ an Integer d such that 6/d is an Integer and d≠3.

Step-by-step explanation:

The original statement is:

∀ integer d, if 6/d is an integer then d=3.

The negation of this statement is:

∃ an Integer d such that 6/d is an Integer and d≠3.

To find the negation, we replace the universal quantifier '∀' with the existential quantifier '∃' and change the implication '→' to 'and'. We also change the conclusion 'd=3' to its negation 'd≠3'.

Therefore, option a. ∃ an Integer d such that 6/d is an Integer and d≠3 is the correct negation.