Question

Find the cardinal number of set P = {x : x = 3n+2, n∈W and x< 15}

Answer 1

P = {x : x = 3n+2, n∈W and x< 15}

For x < 15, n ∈ W :

3n + 2 < 15

3n < 15 - 2

3n < 13

n < 13/3

n < 4.3

Since n has to a natural number, n can only be 1, 2, 3 or 4

⇒ There are 4 elements

Answer: n(P) = 4

Answer 2

Hi ,

It is given that ,

P = { x:x = 3n + 2 ,n € W and x<15 }

Here , x = { 1 , 2 , 3 , .....,14 }

x = 3n + 2

=> 3n + 2 = x

=> 3n = x - 2

n = ( x - 2 )/3 -----( 1 )

___________________

x | n = ( x - 2 )/3 | n € W

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1 | n = (1-2)/3=-1/2 | false

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2| n=(2-2)/3=o | True

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3 | n=(3-2)/3=1/3| false

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4 | n=(4-2)/3=2/3| false

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5 | n=(5-2)/3=3/3 = 1 | True

____________________

6 | n=(6-2)/3=4/2 | false

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7| n = (7-2)/3=5/2 | false

_____________________

8 | n = (8-2)/3 =6/3 = 2 |true

_____________________

9 | n = (9-2)/3=7/3 | false

_____________________

10| n=(10-2)/3 = 8/3 | false

_____________________

11 | n = (11-2)/3=9/3 = 3 | true

_____________________

12 | n = (12-2)/3 = 10/3 | false

_____________________

14 | n = ( 13-2)/3 = 11/3 | false

______________________

Therefore ,

P ={ 2 , 5 , 8 , 11 }

Cardinal number of Set P

= n( P ) = 4

I hope this helps you.

: )