Translate the following statements into symbolic form.(i) Rahul passed

1.	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» p: Rahul passed in Hindi. q: Rahul passed in English. p ∧ q: Rahul passed in Hindi and English. (ii) p: x is even integers. . q : y is even integers. p ∧ q: x andy are even integers. (iii) p: 2 is factor of 12. q: 3 is factor of 12. r: 6 is factor of 12. p ∧ q ∧ r: 2, 3 and 6 are factors of 12 (iv) p: x is an odd integer. q: (x + 1) is an odd integer. p v q: Either x or (x + 1) is an odd integer. (v) p: A number is divisible by 2. q: A number is divisible by 3. pv q: A number is either divisible by 2 or 3. (vi) p: x = 2 is a root of 3x² – x – 10 = 0. q: x = 3 is a root of 3x² – x – 10 = 0 p v q: Either x = 2 or x = 3 is a root of 3x² – x – 10 = 0 (vii) p: Students can take Hindi as an optional paper. q: Students can take English as an optional paper. p v q: Students can take Hindi or English as an optional paper.

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»

p: Rahul passed in Hindi.

q: Rahul passed in English. p ∧ q: Rahul passed in Hindi and English.

(ii) p: x is even integers. . q : y is even integers.

p ∧ q: x andy are even integers.

(iii) p: 2 is factor of 12. q: 3 is factor of 12. r: 6 is factor of 12.

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

(iv) p: x is an odd integer.

q: (x + 1) is an odd integer. p v q: Either x or (x + 1) is an odd integer.

(v) p: A number is divisible by 2. q: A number is divisible by 3.

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

(vi) p: x = 2 is a root of 3x² – x – 10 = 0. q: x = 3 is a root of 3x² – x – 10 = 0

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

(vii) p: Students can take Hindi as an optional paper. q: Students can take English as an optional paper.

p v q: Students can take Hindi or English as an optional paper.