If A- B- C and D be four sets such that A -2-4-6-8-10-12- B -3-6-9-12-15- C -1-4-7-10-13-16 and D - x - x - N -then the number of elements in - A - B - C - - D is

Given: A = {2, 4, 6, 8, 10, 12}, B = {3, 6, 9, 12, 15}, C = {1, 4, 7, 10, 13, 16} and nbsp; D = {x:x∈ℕ} (A∪ B) = {2, 3, 4, 6, 8, 9, 10, 12, 15} (A∪ B)∪ C nb ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Intersection

If A, B, C an...

Question

If $A, B, C$ and $D$ be four sets such that $A = {2, 4, 6, 8, 10, 12}, B = {3, 6, 9, 12, 15}$ , $C = {1, 4, 7, 10, 13, 16}$ and $D = {x : x \in N}$ , then the number of elements in $[(A \cup B) \cup C] \cap D$ is

Open in App

Solution

Given:
$A = {2, 4, 6, 8, 10, 12}$ ,
$B = {3, 6, 9, 12, 15}$ ,
$C = {1, 4, 7, 10, 13, 16}$ and
$D = {x : x \in N}$
$(A \cup B) = {2, 3, 4, 6, 8, 9, 10, 12, 15}$
$(A \cup B) \cup C = {1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 15, 16}$
$[(A \cup B) \cup C] \cap D = {1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 15, 16}$
Number of elememts $= 13$

Suggest Corrections

Similar questions

Q. If

A, B, C

and

D

be four sets such that

A = {2, 4, 6, 8, 10, 12}, B = {3, 6, 9, 12, 15}

C = {1, 4, 7, 10, 13, 16}

and

D = {x : x \in N}

, then the number of elements in

[(A \cup B) \cup C] \cap D

Q. Let

A

and

B

be two sets such that

A \times B

Consists of

6

elements. If three elements of

A \times B

are

(1, 4), (2, 6), (3, 6)

then

B \times A

. is

= {(a, 1), (6, 1), (4, d), (c, 2), (4, 3) (b, 3)}

. Find

a + b + c + d

Q. Let

A

be a non-empty set such that

A \times A

has

16

elements among which three elements are found to be

(a, b), (b, c)

and

(c, d)

and

I_{A}

be the identity relation on

A,

then

Q. Let

A, B, C

and

D

be four non-empty sets. The contrapositive statement of "If

A \subseteq B

and

B \subseteq D

, then

A \subseteq C

" is :

Q. If

A = {x : x

is a natural number

}, B = {x : x

is an even natural number

} C = {x : x

is an odd natural number

}

and

D = {x : x

is a prime number

},

find
(i)

A \cap B

(ii)

A \cap C

(iii)

A \cap D

(iv)

B \cap C

(v)

B \cap D

(vi)

C \cap D

Join BYJU'S Learning Program

If A,B,C and D be four sets such that A={2,4,6,8,10,12},B={3,6,9,12,15}, C={1,4,7,10,13,16} and D={x:x∈N}, then the number of elements in [(A∪B)∪C]∩D is

Given: A={2,4,6,8,10,12}, B={3,6,9,12,15}, C={1,4,7,10,13,16} and D={x:x∈N} (A∪B)={2,3,4,6,8,9,10,12,15} (A∪B)∪C={1,2,3,4,6,7,8,9,10,12,13,15,16} [(A∪B)∪C]∩D={1,2,3,4,6,7,8,9,10,12,13,15,16} Number of elememts =13

If $A, B, C$ and $D$ be four sets such that $A = {2, 4, 6, 8, 10, 12}, B = {3, 6, 9, 12, 15}$ , $C = {1, 4, 7, 10, 13, 16}$ and $D = {x : x \in N}$ , then the number of elements in $[(A \cup B) \cup C] \cap D$ is