Suppose that P(n) is a propositional function. Determine for which improper subset of the domain of n the statement P(n) must be true if a) P(0) is true; for all nonnegative integers n, if P(n) is true, then P(n 2) is true. b) P(0) and P(1) are true; for all nonnegative integers n, if P(n) and P(n 1) are true, then P(n 2) is true

a) P(n) is true for all 'n' in the set ; { 0,2,4,6,8 ….. }

b) P(n) is true for all 'n' in the set ; { 0,1,2,3,4,5 }

Step-by-step explanation:

a) As P(0) is true

we will assume that

this simply means  that ;  P(n) is true for all 'n' in the set

{ 0,2,4,6,8 ….. }

b) since P(0) and P(1) are true

we will assume that

also P(1) and P(2) are true

we will assume that

Also from the previous answers it can be seen that P(2) + P(3) is true

we will assume

This simply means that P(n) is true for all 'n' in the set

{ 0,1,2,3,4,5 }

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step-by-step explanation:

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step-by-step explanation: