Split each of the following into simple sentences and determine whether

Solution:

(i) p: The sum of 3 and 7 is 10 or 11.

q: The sum of 3 and 7 is 10 .

r: The sum of 3 and 7 is 11 .

First sentence is TRUE. Second sentence is FALSE.

Or used is 'Exclusive or'.

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

$\mathrm{q}:(1+\mathrm{i})$ is a real number.

$r:(1+i)$ is a complex number.

First sentence is TRUE. Second sentence is FALSE.

Or used is 'Exclusive or'.

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

q: Every quadratic equation has one real root.

r: Every quadratic equation has two real roots.

Both the sentences are FALSE. So, the compound sentence itself is FALSE.

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

q: You are wet when it rains.

r: You are wet when you are in a river.

Both the component sentences are TRUE.

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

(v) p: 24 is a multiple of 5 or $8 .$

$\mathrm{q}: 24$ is a multiple of $5 .$

$\mathrm{r}: 24$ is a multiple of $8 .$

First sentence is FALSE. Second sentence is TRUE.

Or used is 'Exclusive or'.

(vi) p: Every integer is rational or irrational.

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q: Every integer is rational.

r: Every integer is irrational.

The first sentence is TRUE. The second sentence is TRUE. But both cannot be TRUE at the same time.

'Or' used is 'Exclusive or'.

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

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

r: For getting a driving license you should have a passport.

Both sentences are TRUE.

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

(viii) p: 100 is a multiple of 6 or $8 .$

q: 100 is a multiple of $6 .$

r: 100 is a multiple of 8 .

Both the sentences are FALSE. So the compound sentence itself is FALSE.

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

q: Square of an integer is positive.

r: Square of an integer is negative.

First sentence is TRUE. Second sentence is FALSE.

Or used is 'Exclusive or'.

(x) p: Sun rises or Moon sets.

q: Sun rises.

r: Moon sets.

Here both the sentences are TRUE, but only one occurs at a time.

So, Or used is 'Exclusive or'.