(A) The set $A$ consists of the letters in the word $\text{FOLLOW}$.Listing the distinct letters,we get $A = \{ F, O, L, W \}$.The set $B$ consists of

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(A) The set $A$ consists of the letters in the word $\text{FOLLOW}$.Listing the distinct letters,we get $A = \{ F, O, L, W \}$.The set $B$ consists of the letters in the word $\text{WOLF}$.Listing the distinct letters,we get $B = \{ W, O, L, F \}$.Since the order of elements in a set does not change the set,and both sets contain the exact same elements $\{ F, O, L, W \}$,the sets are equal.Therefore,$A = B$.

Class 11 Mathematics Set Theory Basic of Set theory

Easy

Are the following pair of sets equal? Give reasons.
$A = \{ x : x \text{ is a letter in the word } \text{FOLLOW} \}$
$B = \{ y : y \text{ is a letter in the word } \text{WOLF} \}$

A
Yes,they are equal.
B
No,they are not equal.
C
Set $A$ is a subset of $B$.
D
Set $B$ is a subset of $A$.

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Basic of Set theory

Consider the sets $\phi, A = \{1, 3\}, B = \{1, 5, 9\}, C = \{1, 3, 5, 7, 9\}$. Insert the symbol $\subset$ or $\not\subset$ between the pair of sets: $B \dots C$.

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List all the elements of the following set:
$C = \{ x : x \text{ is an integer; } x^2 \le 4 \}$

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Make correct statements by filling in the symbols $\subset$ or $\not\subset$ in the blank spaces:
${2,3,4} \dots {1,2,3,4,5}$

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If $A$ and $B$ are two sets,then $A \cup B = A \cap B$ if and only if

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Let $A$ and $B$ be sets. If $A \cap X = B \cap X = \phi$ and $A \cup X = B \cup X$ for some set $X$,show that $A = B$. (Hint: Use $A = A \cap (A \cup X)$,$B = B \cap (B \cup X)$ and the Distributive law.)

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Are the following pair of sets equal? Give reasons.$A = \{ x : x \text{ is a letter in the word } \text{FOLLOW} \}$$B = \{ y : y \text{ is a letter in the word } \text{WOLF} \}$

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Consider the sets $\phi, A = \{1, 3\}, B = \{1, 5, 9\}, C = \{1, 3, 5, 7, 9\}$. Insert the symbol $\subset$ or $\not\subset$ between the pair of sets: $B \dots C$.

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Are the following pair of sets equal? Give reasons.
$A = \{ x : x \text{ is a letter in the word } \text{FOLLOW} \}$
$B = \{ y : y \text{ is a letter in the word } \text{WOLF} \}$

List all the elements of the following set:
$C = \{ x : x \text{ is an integer; } x^2 \le 4 \}$

Make correct statements by filling in the symbols $\subset$ or $\not\subset$ in the blank spaces:
${2,3,4} \dots {1,2,3,4,5}$