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The Boolean expression $\sim (p\Rightarrow (\sim q))$ is equivalent to :

• Option 1)

$p \wedge q$

• Option 2)

$q\Rightarrow \sim p$

• Option 3)

$p\vee q$

• Option 4)

$(\sim p)\Rightarrow q$

1

For any two statements $p$ and $q$ , the negation of the expression $p\vee \left ( \sim p\wedge q \right )$ is :

• Option 1)

$\sim p\; \wedge \sim q$

• Option 2)

$p\; \wedge q$

• Option 3)

$p\; \leftrightarrow q$

• Option 4)

$\sim p\; \vee \sim q$

Option 1)      Option 2)       Option 3) Option 4)

Which one of the following statements is not a tautology?

• Option 1)

$(p \vee q)\rightarrow (p\vee (-q))$

• Option 2)

$(p\wedge q)\rightarrow (\sim p)\vee q$

• Option 3)

$p\rightarrow (p\vee q)$

• Option 4)

$(p\wedge q)\rightarrow p$

Option 1) Option 2) Option 3) Option 4)

If the truth value of the statement $p\rightarrow \left ( \sim q\vee r \right )$ is false (F), then the truth values of the statements p, q, r are respectively :

• Option 1)

$F,T,T$

• Option 2)

$T,F,F$

• Option 3)

$T,T,F$

• Option 4)

$T,F,T$

Option 1) Option 2) Option 3) Option 4)

Which one of the following Boolean expressions is a tautology?

• Option 1)

$(p\wedge q)\vee (p\wedge \sim q)$

• Option 2)

$(p\vee q)\vee (p\vee \sim q)$

• Option 3)

$(p\vee q)\wedge (p\vee \sim q)$

• Option 4)

$(p\vee q)\wedge (\sim p\vee \sim q)$

1.)     2.)  3.)  not tautology (take both p & q as T ) 4.)  not tautology (take both p & q as T ) So, option (2) is correct. Option 1) Option 2) Option 3) Option 4)

If $P\Rightarrow (q\vee r)$  is false , then the truth values of $p,q,r$ are respectively :

• Option 1)

$F,T,T$

• Option 2)

$T,F,F$

• Option 3)

$T,T,F$

• Option 4)

$F,F,F$

is false  truth value of p,q,r                                                option =2   Option 1) Option 2) Option 3) Option 4)

The contrapositive of the statement " If you are born in India, then you are a citizen of India", is :

• Option 1)

If you are not born in India, then you are not a citizen of India.

• Option 2)

If you are not a citizen of India, then you are not born in India.

• Option 3)

If you are a citizen of India, then you are born in India.

• Option 4)

If you are born in India, then you are not a citizen of India.

contrapositive If you are not a citizen of India, then you are not born in India. Option 1) If you are not born in India, then you are not a citizen of India. Option 2) If you are not a citizen of India, then you are not born in India. Option 3) If you are a citizen of India, then you are born in India. Option 4) If you are born in India, then you are not a citizen of India.

Contrapositive of the statement ''If two numbers are not equal, then their squares are not equal.'' is:

• Option 1)

If the squares of two numbers are equal, then the numbers are equal.

• Option 2)

If the squares of two numbers are not equal, then the numbers are not equal.

• Option 3)

If the squares of two numbers are equal, then the numbers are not equal.

• Option 4)

If the squares of two numbers are not equal, then the numbers are equal.

Negation - An Assertion that a statement fails or denial of a statement. - wherein P: Delhi is in India  P: Delhi is not in India Contrapositive of   is       Proving by Contradition - When given a statement p is true, we assume that p is not true i.e. ~ p is true. -    Option 1)If the squares of two numbers are equal, then the numbers are equal.Option 2)If the squares of two numbers are not...

The expression $\sim \left ( \sim p\rightarrow q\right )$ is logically equivalent to :

• Option 1)

$p\wedge q$

• Option 2)

$\sim p\wedge q$

• Option 3)

$p\wedge\sim q$

• Option 4)

$\sim p\wedge\sim q$

Truth Table of "NOT" operator - -   Truth Table of "if-then" - -      Option 1)       Option 2)  Option 3)  Option 4)

If q is false and $p\wedge q\leftrightarrow r$  is true, then which one of the following statements is a tautology?

• Option 1)

$(p \vee r)\rightarrow (p\wedge r)$

• Option 2)

$p\wedge r$

• Option 3)

$p \vee r$

• Option 4)

$(p \wedge r)\rightarrow (p\vee r)$

Tautology - A statement pattern is called tautalogy, if it is always true, whatever may be the truth values of constitute statements. -     Truth Table of 'AND' operator - -     Truth Table of "if and only if" - -     Truth table of 'OR' operator - -      is true Case 1   is true and r is true It is not possible as q is false Case 2    is false and r is false  which may be T/F which is...

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)

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

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. -     Truth value of "And"...

The Boolean expression $\left ( \left ( p\wedge q \right )\vee \left ( p\: \vee \sim q \right ) \right )\wedge \left ( \sim p\: \wedge \sim q \right )$ is equivalent to :

• Option 1)

$\left ( \sim p \right )\wedge \left ( \sim q \right )$

• Option 2)

$p\wedge q$

• Option 3)

$p\vee \left ( \sim q \right )$

• Option 4)

$p\wedge \left ( \sim q \right )$

Negation of Conditional Statement - -   Construction of truth table - We prepare table of rows and columns. We write variables denoting sub-statements and we write the truth value of sub statement to get compound statement. - wherein   Option 1)      Option 2)Option 3)Option 4)

The logical statement

$[\sim(\sim p\vee q)\vee (p\wedge r)]\wedge (\sim q \wedge r)$

is equivalent to :

• Option 1)

$(\sim p \wedge \sim q)\wedge r$

• Option 2)

$(p\wedge \sim q) \vee r$

• Option 3)

$\sim p \vee r$

• Option 4)

$(p \wedge r) \wedge \sim q$

Truth value of "And" Conjuction - The statement  has the truth value T whenever both p and q have the truth value T. -     Truth Value of Disjunction "OR" - The statement pq has the truth value F if both p and q have the truth value F. -     Negation of a Statement - Negation is a connective although it doesn't combine two or more statements -   Given, Option 1)  Option 2)  Option 3)  Option 4)

If the Boolean expression $(p\oplus q) \wedge (\sim p \odot q)$ is equivalent to $p \wedge q$ , where  $\oplus, \odot \in \{ \wedge, \vee\}$, then the ordered pair $(\oplus, \odot)$ is:

• Option 1)

$(\wedge, \vee)$

• Option 2)

$(\vee,\vee)$

• Option 3)

$(\vee, \wedge)$

• Option 4)

$(\wedge,\wedge)$

Truth value of "And" Conjuction - The statement  has the truth value T whenever both p and q have the truth value T. -     Truth Value of Disjunction "OR" - The statement pq has the truth value F if both p and q have the truth value F. -     Negation of a Statement - Negation is a connective although it doesn't combine two or more statements - Make truth...
Engineering
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If  $(p \: \wedge \sim q) \wedge (p\wedge r) \rightarrow \sim p \vee q$ is false, then the truth values of p, q and r are, respectively :

• Option 1)

F,T,F

• Option 2)

T,F,T

• Option 3)

T,T,T

• Option 4)

F,F,F

As we learned Truth Table of "if-then" - -       for  to be 0  pqr must be (TFT) or (TFF) Option 1) F,T,F Option 2) T,F,T Option 3) T,T,T Option 4) F,F,F
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