Question

Q8.Answer, whether the following statements are true or false. Give reasons.

(i) The set of even natural numbers less than 21 and the set of odd natural numbers less than 21 are equivalent sets.

(ii) If E = (factors of 16) and F = {factors of 20), then E=F

(iii) The set A = {(integers less than 20) is a finite set.


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answered May 3, 2019 by navnit40 (-4,938 points)

(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.