Answer Whether Following Statements Are True Or False Give Reasons

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.