SOLUTION: Use the De Morgan law that states: ~(p\/q) is equivalent to ~p V ~q to write an equivalent English state ment for the statement. It is not true that apples and beets are

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Question 1019060: Use the De Morgan law that states:


~(p\/q) is equivalent to ~p V ~q to write an equivalent English state ment for the statement.
It is not true that apples and beets are both fruits.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
if you have trouble with the symbols, just write it out in english.

demorgan's laws states:

not (A or B) = not A and not B.

not (A and B) = not A or not B.

your problem statement is:

~(p\/q) is equivalent to ~p V ~q to write an equivalent English state ment for the statement.
It is not true that apples and beets are both fruits.

i translated this to:

not (p and q) is equivalent to not p or not q.

assuming that's true, then the english statement of:

it is not true that apples and beets are both fruits

can also be stated as:

it is not true that apples are not fruits or that beets are not fruits.

this follows the form of demorgan's law shown above, that is:

not (A and B) = not A or not B.