True False[1 Marks ]

Question 511 Mark

Let A = {{1, 2,3}, {4, 5}, {6, 7, 8}}. Then the following is true or false:
$\phi\subset\text{A}.$

Answer

True.Explanation:
$\because\phi$ is a subset of every set, and hence a subset of A.

Question 521 Mark

The given statements is corect? Write a correct form of the given incorrect statements.
$\text{a}\in\{\{\text{a}\}, \text{b}\}$

Answer

False.Explanation:
$\because$ a is not an element of {{a}, b} The correct form is $\text{a}\in\{\{\text{a}\}, \text{b}\}.$

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Question 531 Mark

Let A = {a, b, {c, d}, e}. Then the following statements is false and why?
$\text{a}\subset\text{A}$

Answer

False.Explanation:
$\because$ a belongs to A and not a subset of A. An element of a set belongs to it whereas a subset of it is contained in it.

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Question 541 Mark

Is it true that for any sets A and $\text{B},\text{ P(A)}\cup\text{P(B)}=\text{P(A}\cup\text{B})$? Justify your answer.

Answer

This is a false statement
Let, A = {1} and B = {2}
Then,
$\text{P(A)}=\{\phi,\{1\}\}$
and $\text{P(A)}=\{\phi,\{2\}\}$
$\therefore\text{ P(A)}\cup\text{P(B)}=\{\phi, \{1\}, \{2\}\}$
Now,
$\text{A}\cup\text{B}=\{1, 2\}$
and $\text{P(A}\cup\text{B})=\{\phi, \{1\}, \{2\}, \{1, 2\}\}$
Hence, $\text{P(A)}\cup\text{P(B)}\not=\text{P(A}\cup\text{B).}$

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Maths True False[1 Marks ]