Answer:
A. d, e, f
Step-by-step explanation:
Suppose there is a triangle DEF in which,
EF = d, DF = e, DE = f, ∠D = 48°, ∠F = 73°,
∵ Sum of all interior angles of a triangle is 180°,
⇒ ∠D + ∠F + ∠E = 180°,
⇒ 48° + 73° + ∠E = 180°,
⇒ 121° + ∠E = 180°,
⇒∠E = 59°,
Now, in a triangle the angle opposite to the largest side is largest, opposite to medium angle is medium and opposite to the smallest side is smallest,
∵ ∠F > ∠E > ∠D
By the above statement,
f > e > d
Hence, FIRST OPTION is correct.
Answer: The required answers are
(a) 69, (b) 21, (c) 21 and (d) 0.
Step-by-step explanation: We are given that the set A has 48 elements and the set B has 21 elements.
(a) To determine the maximum possible number of elements in A ∪ B.
If the sets A and B are disjoint, that is they do not have any common element. Then, A ∩ B = { } ⇒ n(A ∩ B) = 0.
From set theory, we have
So, the maximum possible number of elements in A ∪ B is 69.
(b) To determine the minimum possible number of elements in A ∪ B.
If the set B is a subset of set A, that is all the elements of set B are present in set A. Then, n(A ∩ B) = 21.
From set theory, we have
So, the minimum possible number of elements in A ∪ B is 21.
(c) To determine the maximum possible number of elements in A ∩ B.
If the set B is a subset of set A, that is all the elements of set B are present in set A. Then, n(A ∩ B) = 21.
So, the maximum possible number of elements in A ∩ B is 21.
(d) To determine the minimum possible number of elements in A ∩ B.
If the sets A and B are disjoint, that is there is no common element in the sets A and B . Then, n(A ∩ B) = 0.
So, the maximum possible number of elements in A ∩ B is 0.
Thus, the required answers are
(a) 69, (b) 21, (c) 21 and (d) 0.
Answer:
x = 6
Step-by-step explanation:
Pardon the bad handwriting
