Answer, whether the following statements are true or false. Give reasons. (i) The set of even natural numbers less than 21 … ) n(A) =…
Answers:
(i) Set of even natural number less than 21
= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}
∴ Cardinal Number of this set = 10
Set of odd natural numbers less than 21
= {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}
∴ Cardinal number of this set = 10
Now, we see that cardinal numbers of both these sets = 10
∴ “The set of even natural numbers less than 21 and the set of odd natural numbers less than 21 are equivalent sets” …….is True statement.
Answer
(ii) E = {Factors of 16} 1 × 16 = 16
= {1, 2, 4, 8, 16} 2 × 8 = 16
4 × 4 = 16
F = {Factors of 20} 1 × 20 = 20
= {1, 2, 4, 5, 10, 20} 2 × 10 = 20
4 × 5 = 20
Now we see that elements of set E and set F are not the same (identical)
∴ “ If E = {Factors of 16} and F = {Factors of 20},
Then E = F” ………..IS A False statement.
(iii) A = {Integers less than 20}
= {19, 18, 17, 16, …….0, -1, -2, -3,…}
∴ “The set A = {Integers less than 20} is a finite set”……
…….is a False statement.
(iv) A = x : x is an even prime number} = {2}
∴ “If A = {X : X is an even prime number},
Then set A is empty” …..is a false statement.
(v) Set of odd prime numbers
= {3, 5, 7, 11, 13, 17, 19, 23,…..}
∴ “The set of odd prime numbers is the empty set”….. is a false statement.
(vi) Integers Square of Integer whole No.
0 : (0)2 = 0 0
±1 : (±1)2 = 1 1
±2 : (±2)2 = 4 2
±3 : (±3)2 = 9 3
±4 : (±4)2 = 16 4
±5 : (±5)2 = 25 5
……. : …… …… ……
……. : …….. …… …….
∴ Set of square of integers
= {0, 1, 4, 9, 16, 25,……}
Set of whole numbers = {0, 1, 2, 3, 4, 5, 6, 7,…}
Hence “ The set of squares of integers and the set of whole numbers are equal …. False statement.
(vii) n(P) = n(M)
It means number of elements of set P
= Number of elements of set M.
∴ Sets P and M are equivalent.
∴ “ If n(p) = n(M), then P ↔ M” is a true statement.
(viii) Set P = set M
It means sets P and M are equal. Equal sets are equivalent also.
∴ Number of elements of set P = Number of elements of set M
∴ “ If set P = Set M, then n(P) = n(M)”
……………… is a True statement.
(ix) n(A) = n(B)
⇒ Number of elements of set A = Number of elements of set B
∴ Given sets are equivalent but not equal.
∴ “n(A) = n(B) ⇒ A = B” ……………..is a False statement.