(A) The statement "All students are hard working" implies that every element of the set $S$ is also an element of the set $H$.This is mathematically r

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(A) The statement "All students are hard working" implies that every element of the set $S$ is also an element of the set $H$.This is mathematically represented as $S \subseteq H$.In terms of Venn diagrams,this means the circle representing set $S$ must be entirely contained within the circle representing set $H$ inside the universal set $U$.This corresponds to the diagram in option $A$.

Class 11 Mathematics Sets Venn Diagram and Operation on Sets

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Which Venn diagram represents the truth of the statement "All students are hard working."
Where $U$ = Universal set of human beings,$S$ = Set of all students,$H$ = Set of all hard workers.

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Venn Diagram and Operation on Sets

If $A = \{3, 6, 9, 12, 15, 18, 21\}$,$B = \{4, 8, 12, 16, 20\}$,$C = \{2, 4, 6, 8, 10, 12, 14, 16\}$,and $D = \{5, 10, 15, 20\}$,find $B - C$.

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If $A, B$ and $C$ are any three sets,then $A - (B \cap C)$ is equal to

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If $A = \{1, 2, 3, 4, 5\}, B = \{2, 4, 6\}, C = \{3, 4, 6\},$ then $(A \cup B) \cap C$ is

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If $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$,$A = \{2, 4, 6, 8\}$ and $B = \{2, 3, 5, 7\}$,verify that $(A \cup B)^{\prime} = A^{\prime} \cap B^{\prime}$.

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If sets $A$ and $B$ are defined as follows:
$A = \{(x, y) : y = \frac{1}{x}, 0 \neq x \in R\}$
$B = \{(x, y) : y = -x, x \in R\}$,then

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Which Venn diagram represents the truth of the statement "All students are hard working."Where $U$ = Universal set of human beings,$S$ = Set of all students,$H$ = Set of all hard workers.

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If $A = \{3, 6, 9, 12, 15, 18, 21\}$,$B = \{4, 8, 12, 16, 20\}$,$C = \{2, 4, 6, 8, 10, 12, 14, 16\}$,and $D = \{5, 10, 15, 20\}$,find $B - C$.

If $A, B$ and $C$ are any three sets,then $A - (B \cap C)$ is equal to

If $A = \{1, 2, 3, 4, 5\}, B = \{2, 4, 6\}, C = \{3, 4, 6\},$ then $(A \cup B) \cap C$ is

If $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$,$A = \{2, 4, 6, 8\}$ and $B = \{2, 3, 5, 7\}$,verify that $(A \cup B)^{\prime} = A^{\prime} \cap B^{\prime}$.

If sets $A$ and $B$ are defined as follows:$A = \{(x, y) : y = \frac{1}{x}, 0 \neq x \in R\}$$B = \{(x, y) : y = -x, x \in R\}$,then

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Which Venn diagram represents the truth of the statement "All students are hard working."
Where $U$ = Universal set of human beings,$S$ = Set of all students,$H$ = Set of all hard workers.

If sets $A$ and $B$ are defined as follows:
$A = \{(x, y) : y = \frac{1}{x}, 0 \neq x \in R\}$
$B = \{(x, y) : y = -x, x \in R\}$,then