Can be more than one correct answer Let U, the universal set, be the set of all

Question

Can be more than one correct answer

Let U, the universal set, be the set of all human beings in history. Let R be the relation on U defined by xRy if and only x is an ancestor of y. Then which of the following propositions are equivalent to "it is not true that any two different people in history shares a common ancestor". exist x not forall y((x notequalto y) rightarrow exist z((zRx)^(zRy))) exist x exist y((x notequalto y)^forall z(not(zRx)^not(zRy)))) There are two different people x and y in history such that any person in history is either not the ancestor of x or not the ancestor of y. There is a person in history who is not the common ancestor of any two different people in history.

Explanation / Answer

b) is true since it says that no two different people in history has a common anscentor.

c) is false since it is not same as that of the condition.

d) is true since it says that there is a person in the history who is not a anscentor of different people in history.which is our condition

a) false.since it says that there exist a z satisfy zRx and zRy.which is not equal.

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