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  • Translate the following statements into symbolic form (i) Rahul passed in Hindi and English.

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 3x^{2}-x-10=0
(vii) Students can take Hindi or English as an optional paper.

Answers (1)

(i) It is a compound statement whose components are –

p: Rahul passed in Hindi &

q: Rahul passed in English

Symbolically, the function is represented as –

p \wedge q – Rahul passed in Hindi & English

(ii) It is a compound statement whose components are –

p: x is an even integer, &

q: y is an even integer

Symbolically, the function is represented as –

p \wedge q -x \; and\; y are even integers.

(iii) It is a compound statement whose components are –

p: 2 is a factor of 12

q: 3 is a factor of 12 &

r: 6 is a factor of 12

Symbolically the function is represented as –

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

(iv) It is a compound statement whose components are –

p: x is an odd integer &

q:x+1 is an odd integer

Symbolically the function is represented as –

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

(v) It is a compound statement whose components are –

p: A number is divisible by 2 &

q: A number is divisible by 3

Symbolically the function is represented as –

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

(vi) It is a compound statement whose components are –

p: x = 2 is a root of 3x^2 - x -10 = 0 &

q: x = 3 is a root of 3x^2 - x -10 = 0

Symbolically, the function is represented as –

p v q – Either x = 2 or x = 3 is a root of 3x^2 - x -10 = 0

(vii) It is a compound statement whose components are –

p: Hindi is the optional paper &

q: English is the optional paper

Symbolically the function is represented as –

p v q – Either Hindi or English is optional paper.

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