MadeEasy Subject Test: Engineering Mathematics - First Order Logic

Question

Which of the following option is correct for the given predicate with domain of all people

    Where F(x, y) means ‘x is a friend of y’.

• If two persons are not friend of each other then they have atleast one friend common.
• If two persons have atleast one common friend then they are not friend of each other.
• Both (a) and (b)
• None of the above

I think the answer should be there exists a person all of his friends are not friends with each other

but the solution says b

Comments

If we take an example of group of people such that there exist one person who is not friends with anyone. Then it will satisfy the above predicate. So ans should be D i guess

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@Pankaj

but what I'm trying to say is I think the question says there is a person x who has two or more friends then  none of them are friends with each other

This is what the option B states. You are also saying the same just in different way.

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no option b says that is true for every common friend but what I'm saying is there just needs to be only one not neccessary for all