**Question:**

**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.**

**Solution:**

**(i) Rahul passed in Hindi and English.**

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) x and y are even integers.**

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) 2, 3 and 6 are factors of 12.**

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) Either x or x + 1 is an odd integer.**

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) A number is either divisible by 2 or 3.**

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) Either x = 2 or x = 3 is a root of 3x 2 – x – 10 = 0**

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

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.