If A={a, b, c, d, e}, B={a, c, e, g} and C={b, d, e, g}, then which of the following is true? (1

If A={a, b, c, d, e}, B={a, c, e, g} and C={b, d, e, g},...

If $\mathrm{A}=\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}\}, \mathrm{B}=\{\mathrm{a}, \mathrm{c}, \mathrm{e}, \mathrm{g}\}$ and $\mathrm{C}=\{\mathrm{b}, \mathrm{d}, \mathrm{e}, \mathrm{g}\}$, then which of the following is true? (1) $\mathrm{C} \subset(\mathrm{A} \cup \mathrm{B})$ (2) $\mathrm{C} \subset(\mathrm{A} \cap \mathrm{B})$ (3) $\mathrm{A} \cup \mathrm{B}=\mathrm{A} \cup \mathrm{C}$ (4) Both (1) and (3)

If $\mathrm{A}=\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}\}, \mathrm{B}=\{\mathrm{a}, \mathrm{c}, \mathrm{e}, \mathrm{g}\}$ and $\mathrm{C}=\{\mathrm{b}, \mathrm{d}, \mathrm{e}, \mathrm{g}\}$, then which of the following is true?
(1) $\mathrm{C} \subset(\mathrm{A} \cup \mathrm{B})$
(2) $\mathrm{C} \subset(\mathrm{A} \cap \mathrm{B})$
(3) $\mathrm{A} \cup \mathrm{B}=\mathrm{A} \cup \mathrm{C}$
(4) Both (1) and (3)

Key Concepts

Set Equality

Set equality occurs when two sets have exactly the same elements, regardless of order or repetition. This concept is used to compare complex set expressions involving operations such as union and intersection.

Intersection

The intersection of two sets is the set containing all elements that are common to both sets, denoted by the symbol ?. It identifies shared elements and is important for understanding overlapping characteristics between sets.

Union

The union of two sets is the set containing all elements that are in either set or in both. This operation, represented by the symbol ?, combines the elements of multiple sets into one larger set.

Subset

A subset is a set in which every element is also contained within another set. This concept is crucial for determining inclusion relationships between sets, often denoted by the symbol ?.

Transcript

00:01 Hello students in this problem the sets a b and c are given and we have to select that which of the following options are correct so let me draw the venn diagram of the three sets here first suppose this is set a this is set b and let it be set c so we can see that the set a contains the element a b cede and we can see that the set a contains the element a b cede and where a and c are common with set b.

00:40 So i will place set elements a and c here.

00:47 Elements a and c are present in both set a and set b.

00:53 Sorry, this would be set b and this would be set c.

00:58 A and c, these two elements are present in a and b both.

01:03 But they are not in the set c so they are outside the circle c now coming to the third element coming to the element b and d we can see that the elements b and c are common in the set a and c so i will place b and d here they are in the set a and in the set c but not in the set b.

01:32 That's why they are outside the circle b and the set and the element e the element e is common in all the sets the element e is common in the all the elements so e will be in all the circles that's why e will be there which is in the set a b and c all three now the set b has the elements a c e and g we can see that g, g, we can see that g, g, element is common in b and c so the element g will be there which is in the set b and c but not in the set a so all the elements are filled now coming to the choice a here written that the set c is subset of a union b this is set c and this is set a union b now we can say that the set c contains b, d, e and g while the set a union b.

02:50 A union b, this set contains b, d, d, g, a c...

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