We will show that the reflexive closure of a transitive closure of a relation is equal to the transitive closure of its reflexive closure through a series of simpler results: [3 marks] let ribe a transitive relation on a set s, show that its reflexive closure rr is also transitive. [3 marks] let rą be a reflexive relation on a set s, show that its transitive closure tr, is also reflexive. [3 marks] using the previous results or otherwise, show that r(tr) = t(rr) for any relation r on a set. hint: you may find the fact that transitive (resp. reflexive) closures of r are the smallest transitive (resp. reflexive) relation containing r useful.

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

answer: b

step-by-step explanation: