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.

(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 ᴧ 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 ᴧ 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 ᴧ q ᴧ 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 ᴧ q: Either Hindi or English is optional paper.