Question

Let p(n): 3n + 10 is a prime number. P(n) is true unen, such that
n>2
n<2
n<4
n> 3​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

Let p(n): 3n + 10 is a prime number. P(n) is true such that

• n > 2

• n < 2

• n < 4

• n > 3

EVALUATION

The given statement is

p(n) : 3n + 10 is a prime number

where n is a natural number

CHECKING FOR n = 1

For n = 1

$\sf{}p(1) = (3 \times 1) + 10$

$\implies \sf{}p(1) = 3+ 10$

$\implies \sf{}p(1) = 13$

Now 13 is a prime number

So the statement p(n) is true fo n= 1

CHECKING FOR n = 2

For n = 2

$\sf{}p(2) = (3 \times 2)+ 10$

$\implies \sf{}p(2) = 6+ 10$

$\implies \sf{}p(2) = 16$

Now 16 is not a prime number

So the statement p(n) is not true for n= 2

So the statement p(n) is true for n= 1 only

FINAL ANSWER

Let p(n): 3n + 10 is a prime number.

P(n) is true such that n < 2

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