Question

The set {x | x = 3p-2, 1 < p < 5 and p ∈ N} is the same as??

Answer 1

Answer:

For mutually exclusive and exhaustive events,

0≤

2

1−3p

≤1,0≤

3

1+4p

≤1,0≤

6

1+p

≤1 and 0≤

2

1−3p

+

3

1+4p

+

6

1+p

≤1

⇒0≤1−3p≤2,0≤1+4p≤3,0≤1+p≤6 and 0≤

6

3(1−3p)+2(1+4p)+1+p

≤1

⇒−1≤−3p≤1,−1≤4p≤2,−1≤p≤5 and 0≤1≤1

⇒−

3

1

≤p≤

3

1

,−

4

1

≤p≤

2

1

,−1≤p≤5

Now taking intersection of above we get p∈[−

4

1

,

3

1

]