Students deliver catalogues and leaflets to houses. One day, they have to deliver 384 catalogues and 1890 leaflets.
Each student can deliver either 16 catalogues or 90 leaflets in 1 hour.
Each student can only work for 8 hours.
All students hired are paid £51.30 per day, even if they don't work a full day.
If the minimum number of students are hired, how much will the wage bill be?

Vacuous proof is used.

Step-by-step explanation:

Given:

Proposition p(n) :

"if n is a positive integer greater than 1, then n² > n"

To prove:

Prove the proposition p (0)

Solution:

Using the proposition p(n) the proposition p(0) becomes:

p(0) = "if 0 is a positive integer greater than 1, then 0² > 0"

The proposition that "0 is a positive integer greater than 1" is false

Since the premises "if 0 is a positive integer greater than 1" is false this means the overall proposition/ statement is true.

Thus this is the vacuous proof which states that:

if a premise p ("0 is a positive integer greater than 1") is false then the implication or conditional statement p->q ("if n is a positive integer greater than 1, then n² > n") is trivially true.

So in vacuous proof, the implication i.e."if n is a positive integer greater than 1, then n2 > n." is only true when the antecedent i.e. "0 is a positive integer greater than 1" cannot be satisfied.