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Question

It says "false as truth value". Means contradiction ???

Comments

Yes .

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false as truth value

means result of statement as false

Answer 1

(a) $\exists x R(x) \vee \forall y[\sim S(y)]$

∃xR(x) : there exists atleast a number such that x-7=2 so x=9 that means this statement is True

∀y[∼S(y)] = ∀y[y $\leqslant$ 9] : all y are less then equal to 9 : False

so T ∨ F = True

 

(b) P(x,y) : x>y

     $\forall x \exists y P(x,y)$ : For every x there is at least one less y , so for domain is real number then this is True 

 

(c) $\forall x \exists y(P(x,y) \cup Q(x,y)) $

     $\forall x \exists y((x>y) OR (x\leqslant y)) : True$

 

So Ans : D