Q: Which of the following is an empty set?

Let's check the options: (A) $\{x : x^2 - 2 = 0 \text{ and } x \text{ is rational}\}$ has no rational solution since $\sqrt{2}$ is irrational. (B) $\{x : x^2 = 4 \text{ and } x \text{ is even}\}$ has solution $x = \pm 2$. (C) $\{x : x \text{ is a real number and } x > x\}$ is always false. Wait, opt

Question 1

Which of the following is a well-defined collection and hence a set?

Accepted Answer

A set is a well-defined collection of objects. The collection of all vowels in the English alphabet is well-defined because anyone can universally determine whether a letter is a vowel or not. The other options depend on personal opinions or preferences, making them not well-defined collections.

Question 2

Write the set $A = \{x : x 	ext{ is an integer and } -3

Accepted Answer

The condition given is that $x$ is an integer strictly greater than $-3$ and strictly less than $7$. The integers satisfying this condition are $-2, -1, 0, 1, 2, 3, 4, 5, 6$. Therefore, the roster form is $\{-2, -1, 0, 1, 2, 3, 4, 5, 6\}$.

Question 3

Which of the following is an empty set?

Accepted Answer

Let's check the options: (A) $\{x : x^2 - 2 = 0 	ext{ and } x 	ext{ is rational}\}$ has no rational solution since $\sqrt{2}$ is irrational. (B) $\{x : x^2 = 4 	ext{ and } x 	ext{ is even}\}$ has solution $x = \pm 2$. (C) $\{x : x 	ext{ is a real number and } x > x\}$ is always false. Wait, opt

Question 4

Which of the following sets is a finite set?

Accepted Answer

A finite set is a set whose elements can be counted. The set of lines parallel to the x-axis is infinite. The set of numbers which are multiples of 5 is infinite. The set of animals living on the earth is finite (though extremely large, it has a definite countable number). The set of all prime numbe

Question 5

If $A = \{1, 2, 3, 4\}$ and $B = \{3, 4, 5, 6\}$, find $A \cup B$.

Accepted Answer

The union of two sets $A$ and $B$ is the set of all elements which are in $A$ or in $B$ or in both. Combining the elements of $A$ and $B$ without repetition gives $A \cup B = \{1, 2, 3, 4, 5, 6\}$.

Sets