Answer
a. years after $2020$
b. years after $2024$
c. years after 2024.
d. years after 2020.
Work Step by Step
a. Use the formula for the interfaith marriage $I=\frac{1}{4}x+26$, for $I\gt 34$, we have $\frac{1}{4}x+26\gt 34$ which gives $\frac{1}{4}x\gt 8$ and $x\gt 32$. Thus the years should be after $1988+32=2020$
b. Use the formula $N=\frac{1}{4}x+6$, for $N\gt 15$, we have $\frac{1}{4}x+6\gt 15$ which gives $\frac{1}{4}x\gt 9$ and $x\gt 36$. Thus the years should be after $1988+36=2024$
c. Find the intersection of the above results, we get $x\gt 36$ which means years after 2024.
d. Find the union of the results in (a) and (b), we get $x\gt 32$ which means years after 2020.