Q. 54.7( 3 Votes )

Translate the following statements into symbolic form

(i) Rahul passed in Hindi and English.

(ii) x and y are even integers.

(iii) 2, 3 and 6 are factors of 12.

(iv) Either x or x + 1 is an odd integer.

(v) A number is either divisible by 2 or 3.

(vi) Either x = 2 or x = 3 is a root of 3x2 – x – 10 = 0

(vii) Students can take Hindi or English as an optional paper.

Answer :

(i)The given sentence is a compound statement in which components are

p:Rahul passed in Hindi


q:Rahul passed in English


Now, It can be represent in symbolic function as,


p q: Rahul passed in Hindi and English.


(ii) The given sentence is a compound statement in which components are


p:x is an even integer


q:y is an even integer


Now, It can be represent in symbolic function as,


p q: x and y are even integers.


(iii) The given sentence is a compound statement in which components are


p:2 is a factor of 12


q:3 is a factor of 12


r: 6 is a factor of 12


Now, It can be represent in symbolic function as,


p q r: 2, 3 and 6 are factors of 12.


(iv) The given sentence is a compound statement in which components are


p:x is an odd integer


q:x+1 is an odd integer


Now, It can be represent in symbolic function as,


p V q: Either x or x + 1 is an odd integer.


(v) The given sentence is a compound statement in which components are


p:A number is divisible by 2


q:A number is divisible by 3


Now, It can be represent in symbolic function as,


p V q: A number is either divisible by 2 or 3.


(vi) The given sentence is a compound statement in which components are


p: x = 2 is a root of 3x2 – x – 10 = 0


q: x = 3 is a root of 3x2 – x – 10 = 0


Now, It can be represent in symbolic function as,


p V q: Either x = 2 or x = 3 is a root of 3x2 – x – 10 = 0


(vii) The given sentence is a compound statement in which components are


p: Hindi is the optional paper


q: English is the optional paper


Now, It can be represent in symbolic function as,


p q: Either Hindi or English is optional paper.


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