Home
Class 12
MATHS
Consider the following statements P: S...

Consider the following statements
P: Suman is brilliant
Q: Suman is rich
R: Suman is honest
The negation of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as

A

`~(p^^R)harrQ`

B

`~p^^(Qharr~R)`

C

`~(Qharr (P^^~R))`

D

`~Q harr~P^^R`

Text Solution

Verified by Experts

The correct Answer is:
C
Suman is brilliant and dishonest is `p^^~R` suman is brilliant and dishonest iff suman is rich is
`Q harr (p^^~R)`
Negative of statement is expressed as
`~(Q harr(P^^~R))`
Promotional Banner

Topper's Solved these Questions

  • MATHMETICAL REASONING

    CENGAGE ENGLISH|Exercise Single correct answer type|38 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE ENGLISH|Exercise JEE ADVANCED|1 Videos

  • MATRICES

    CENGAGE ENGLISH|Exercise Single correct Answer|34 Videos

Similar Questions

Explore conceptually related problems

Compare the following statements : p, only if q.

Consider the following statements. p : Hari is clever. q: shyam is fool. r: Shyam is honest. The negation of statement Hari is clever & Shyam is dishonest if and only if shyam is fool is expressed. As.... (1) ~p^^(q⇔~ r) (2) ~(q ⇔(p^^~r)) (3) ~ q ⇔(~ p^^r ) (4) ~(p^^~ r) (5) ~(p^^r)

Negation of the statement ~ p to (q vv r) is

Negation of the statement (p ^^ r) -> (r vv q) is-

Consider the following statements : p: He is intelligent q: He is strong Then symbolic form of statements 'it is wrong that he is intelligent or strong's

Consider the following statement : p : I shall pass, q : I study, then write the verbal translation of the symbolic representation p hArr q .

Consider the following statements: p : I shall pass, q : I study The symbolic represention of the proposition " I shall pass iff I study" is

Statement 1 : Consider the statements p : Delhi is in India q : Mumbai is not in Italy Then the negation of the statement p vv q , is 'delhi is not in India and Mumbai is in Italy' Statement 2: For any two statement p and q ~(p vv q) = ~p vv ~q

Write the following statement in the form if p then q : It rains only if it is cold.

Given two statements p: Suman is healthy. q: She eats healthy food. Then p∨q means