Class 11 Mathematics Set Theory Complement of a Set

Easy

Taking the set of natural numbers as the universal set,write down the complement of the following set:
$A = \{x: 2x + 5 = 9\}$

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Solution

(N/A) Given the universal set $U = N$ (the set of natural numbers).
Let the set be $A = \{x: 2x + 5 = 9\}$.
Solving the equation: $2x + 5 = 9 \implies 2x = 4 \implies x = 2$.
So,$A = \{2\}$.
The complement of set $A$ is $A' = U - A = \{x: x \in N \text{ and } x \neq 2\}$.

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Set Theory

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Complement of a Set

Let $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ and $A = \{1, 3, 5, 7, 9\}$. Find $A^{\prime}$.

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$A:$ getting an even number on the first die.
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Taking the set of natural numbers as the universal set,write down the complement of the following set:$A = \{x: 2x + 5 = 9\}$

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Taking the set of natural numbers as the universal set,write down the complement of the following set:
$A = \{x: 2x + 5 = 9\}$

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
Describe the event $\text{not } B$.

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
Describe the event $A^{\prime}$.