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 3x2 – x – 10 = 0
(vii) Students can take Hindi or English as an optional paper.
1 Answers
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.