(i) The sum of 3 and 7 is 10 or 11.

Let p: The sum of 3 and 7 is 10.

And q: The sum of 3 and 7 is 11.

First sentence is TRUE. Second sentence is FALSE.

Or used is ‘Exclusive or’.

(ii) (1 + i) is a real or a complex number.

Let q: (1 + i) is a real number.

And q: (1 + i) is a complex number.

First sentence is TRUE. Second sentence is FALSE.

Or used is ‘Exclusive or’.

(iii) Every quadratic equation has one or two real roots.

Let q: Every quadratic equation has one real root.

And q: Every quadratic equation has two real roots.

P and q both are False.

Given sentence is FALSE.

(iv) You are wet when it rains, or you are in a river.

Let p: You are wet when it rains.

And q: You are wet when you are in a river.

(p or q) is true.

Or used is ‘Inclusive or’ because you can get wet either it rains or when you are in the river.

(v) 24 is a multiple of 5 or 8.

Let p: 24 is a multiple of 5.

And q: 24 is a multiple of 8.

First sentence is FALSE. Second sentence is TRUE.

Or used is ‘Exclusive or’.

(vi) Every integer is rational or irrational.

Let p: Every integer is rational.

And q: Every integer is irrational.

(p or q) is true.

‘Or’ used is ‘Exclusive or’.

(vii) For getting a driving license you should have a ration card or a passport.

Let p: For getting a driving license you should have a ration card.

And q: For getting a driving license you should have a passport.

(p or q) is true.

Or used is ‘Inclusive or’, because you can get a driving license with ration card or with passport or when they have both.

(viii) 100 is a multiple of 6 or 8.

Let p: 100 is a multiple of 6.

And q: 100 is a multiple of 8.

(p or q) is FALSE.

(ix) Square of an integer is positive or negative.

Let p: Square of an integer is positive.

And q: Square of an integer is negative.

(p or q) is FALSE.

(x) Sun rises or Moon sets.

Let p: Sun rises.

And q: Moon sets.

(p or q) is TRUE.

Here, Or used is ‘Exclusive or’.