Fill In The Blanks[1 Marks ]

Question 11 Mark

The set $\{\text{x} \in \text{R} : 1 \leq \text{x} < 2\}$ can be written as ______________.

Answer

The set $\{\text{x} \in \text{R} : 1 \leq \text{x} < 2\}$ can be written as [1, 2).
Solution:
The set $\{\text{x}\in\text{R}:1\leq\text{x}<2\}$ can be written as [1, 2).
Hence, the filler is [1, 2).

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Question 21 Mark

Power set of the set A = {1, 2} is ______________.

Answer

Power set of the set A = {1, 2} is $\big\{\{1\},\{2\},\{1,2\},\phi\}$.
Solution:
Power set of $\text{A}=\text{p(A)}=\big\{\{1\},\{2\},\{1,2\},\phi\big\}.$
Hence, the filler is $\big\{\{1\},\{2\},\{1,2\},\phi\}.$

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Question 31 Mark

If A and B are finite sets such that $\text{A}\subset\text{B},$ then $\text{n} (\text{A} \cup \text{B})$ = ______________.

Answer

If A and B are finite sets such that $\text{A}\subset\text{B}$ then $\text{n}(\text{A}\cup\text{B})=\text{n(B)}.$
Solution:
Since $\text{A}\subset\text{B}\therefore \text{n}(\text{A}\cup\text{B})=\text{n(B)}$
Hence, the filler is n(B).

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Question 41 Mark

If $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}, A = \{1, 2, 3, 5\}, B = \{2, 4, 6, 7\}$ and $C = \{2, 3, 4, 8\}.$ Then

$(\text{B} \cup \text{C})'$ is $............$
$(C - A)'$ is $............$

Answer

If $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}, A = \{1, 2, 3, 5\}, B = \{2, 4, 6, 7\}$ and $C = \{2, 3, 4, 8\}.$ Then

$(\text{B} \cup \text{C})'$ is $\{1, 5, 9, 10\}.$
$(C – A)'$ is $\{1, 2, 3, 5, 6, 7, 9, 10\}.$

Solution:
Given that: $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\},$
$A = \{1, 2, 3, 5\}, B = \{2, 4, 6, 7\}$ and $C = \{2, 3, 4, 8\}$

$(\text{B}\cup\text{C})'=\{2,3,4,6,7,8\}'=\{1,5,9,10\}$

Hence, the filler is $\{1, 5, 9, 10\}.$

$(\text{C}-\text{A})'=\{4,8\}'=\{1,2,3,5,6,7,9,10\}$

Hence, the filler is $\{1, 2, 3, 5, 6, 7, 9, 10\}.$

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Question 51 Mark

Given the sets A = {1, 3, 5}. B = {2, 4, 6} and C = {0, 2, 4, 6, 8}. Then the universal set of all the three sets A, B and C can be ______________.

Answer

Given the sets A = {1, 3, 5}. B = {2, 4, 6} and C = {0, 2, 4, 6, 8}. Then the universal set of all the three sets A, B and C can be {0, 1, 2, 3, 4, 5, 6, 8}.
Solution:
Given that: A = {1, 3, 5}. B = {2, 4, 6} and C = {0, 2, 4, 6, 8}
$\therefore$ Universal set of all the given sets is
U = {0, 1, 2, 3, 4, 5, 6, 8}
Hence, the filler is {0, 1, 2, 3, 4, 5, 6, 8}.

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Question 61 Mark

When $\text{A}=\phi,$ then number of elements in P(A) is ______________.

Answer

When $\text{A}=\phi,$ then number of elements in P(A) is 1.
Solution:
Here $\text{A}=\phi \therefore \text{n(A)}=0$
$\because \text{n}[\text{P(A)}]=2^{\text{n(A)}}=2^0=1$
Hence, the filler is 1.

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Question 71 Mark

For all sets A and B, $\text{A} - (\text{A} \cap \text{B})$ is equal to ______________.

Answer

For all sets A and B, $\text{A} - (\text{A} \cap \text{B})$ is equal to $\text{A}\cap\text{B}'.$
Solution:
Since $\text{A}-\text{B}=\text{A}\cap\text{B}'$
$\Rightarrow \text{A}-(\text{A}\cap\text{B})=\text{A}\cap\text{B}'$

Hence, the filler is $\text{A}\cap\text{B}'.$

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Question 81 Mark

If A and B are any two sets, then A - B is equal to ______________.

Answer

If A and B are any two sets, then A - B is equal to $\text{A}\cap\text{B}'$.
Solution:
From the Venn diagram it is clear that

$\text{A}-\text{B}=\text{A}\cap\text{B}'$
Hence the filler is $\text{A}\cap\text{B}'.$

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Maths Fill In The Blanks[1 Marks ]

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