Question

3. The set {x: x is a positive integer less than 6 and 3* – 1 is an even number} in roster form is
(a) {1,2,3,4,5)
(b) {1, 2, 3. 4. 5. 6)
(C) 2.4.6)
(d) {1.3.5)​

Answer 1

Answer:

Option a is the correct answer.

Because less than 6 are 1,2,3,4,5 and 3-1=2 this is even number.

So the answer is x={1,2,3,4,5}

Hope you understand.

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

The set

$\sf \{x : x \: is \: an \: positive \: integer \: less \: than \: 6 \: and \: ({3}^{x} - 1) \: is \: an \: even \: number \}$

(a) {1,2,3,4,5}

(b) {1, 2, 3. 4. 5. 6}

(c) {2, 4, 6}

(d) {1, 3, 5 }

EVALUATION

Let S be the given set

Then

$\sf S = \{x : x \: is \: an \: positive \: integer \: less \: than \: 6 \: and \: ({3}^{x} - 1) \: is \: an \: even \: number \}$

The positive integers less than 6 are 1 , 2 , 3 , 4 , 5

$\sf For \: x = 1 \: , {3}^{x} - 1=0 \: which \: is \: even \: integer$

∴ 1 ∈ S

$\sf For \: x = 2 \: , {3}^{x} - 1=8 \: which \: is \: even \: integer$

∴ 2 ∈ S

$\sf For \: x = 3 \: , {3}^{x} - 1=26 \: which \: is \: even \: integer$

∴ 3 ∈ S

$\sf For \: x = 4 \: , {3}^{4} - 1=80 \: which \: is \: even \: integer$

∴ 4 ∈ S

$\sf For \: x = 5 \: , {3}^{x} - 1=242 \: which \: is \: even \: integer$

∴ 5 ∈ S

∴ S = { 1 , 2 , 3 , 4 , 5 }

FINAL ANSWER

Hence the correct option is

(a) { 1 , 2 , 3 , 4 , 5 }

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