(i) Given: The open sentence x + 2 < 10 is defined on N.

Here N: {1, 2, 3, 4, 5, 6, 7, 8, …….…}

At x = 1 ⇒ x + 2 = 3 < 10

At x = 2 ⇒ x + 2 = 4 < 10

At x = 3 ⇒ x + 2 = 5 < 10

At x = 4 ⇒ x + 2 = 6 < 10

At x = 5 ⇒ x + 2 = 7 < 10

At x = 6 ⇒ x + 2 = 8 < 10

At x = 7 ⇒ x + 2 = 9 < 10

At x = 8 ⇒ x + 2 = 10

x = {1, 2, 3, 4, 5, 6, 7} satisfies x + 2 <10.

So, the truth set of open sentence x + 2 < 10 defined on N : {1, 2, 3, 4, 5, 6, 7}

(ii) The open sentence x + 5 < 4 is defined on N.

Here N: {1, 2, 3, 4, 5, 6, 7, 8, …….…}

At x = 1 ⇒ 1 + 5 = 6 > 4

So, the truth set of open sentence x + 5 < 4 defined on N is an empty set, {}.

(iii) The open sentence x + 3 > 2 is defined on N.

Here N: {1, 2, 3, 4, 5, 6, 7, 8, …….…}

At x = 1 ⇒ x + 3 = 4 > 2

At x = 2 ⇒ x + 3 = 5 > 2

At x = 3 ⇒ x + 3 = 6 > 2

At x = 4 ⇒ x + 3 = 7 > 2

At x = 5 ⇒ x + 3 = 8 > 2

At x = 6 ⇒ x + 3 = 9 > 2

At x = 7 ⇒ x + 3 = 10 > 2

And so on…

x = {1, 2, 3, 4, 5, 6, 7….} satisfies x + 3 > 2.

So, the truth set of open sentence x + 3 > 2 defined on N is an infinite set i.e. {1, 2, 3, 4, 5, 6, 7, ………}