# Consider the following three statements :P    :    5 is a prime number.Q    :    7 is a factor of 192.R    :    L.C.M of 5 and 7 is 35.Then the truth value of which one of the following statement is true?Option 1)$(\sim P) \vee (Q\wedge R)$Option 2)$(\sim P) \wedge (Q\wedge R)$Option 3)$P \vee (\sim Q\wedge R)$Option 4)$(P\wedge Q)\vee (\sim R)$

S Shipra

P:5 is a prime number  is true statement

Q:7is a factor of 192, is false statement

R:LCM of 5 and 7 is a35, is true statement

1. So ,truth value of P is T, Q is F, R is T

Truth set -

The set of all those values of variable in an open statement for which it becomes a true statement.

- wherein

For example: x2 -3x+2=0
Truth set {1,2}

'And' Conjunction -

Normally the conjunction 'and' is used between two statements which have some kind of relation but in logic, it can be used even if there is no relation between the statements.

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Truth value of "And" Conjuction -

The statement $p\wedge q$ has the truth value T whenever both p and q have the truth value T.

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Disjunction "OR" -

The symbol for "OR" disjunction is the symbol $\vee$

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Truth Value of Disjunction "OR" -

The statement p$\vee$q has the truth value F if both p and q have the truth value F.

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Negation -

An Assertion that a statement fails or denial of a statement.

- wherein

P: Delhi is in India

$\sim$P: Delhi is not in India

P is true

Q is false

R is true

(1) $(\sim P)\vee (Q\wedge R)=F$

(2) $(\sim P)\wedge (\sim Q\wedge R)=F$

(3) $P\vee (\sim Q\wedge R)=T$

(4) $(P\wedge Q)\vee(\sim R)=F$

Option 1)

$(\sim P) \vee (Q\wedge R)$

Option 2)

$(\sim P) \wedge (Q\wedge R)$

Option 3)

$P \vee (\sim Q\wedge R)$

Option 4)

$(P\wedge Q)\vee (\sim R)$

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