Thanks for the question! So this question tells us how to approach it: let’s start off by picking Z, and see what inferences we should make! Now, we should notice that some of these rules are related to each other. Let’s see if there’s any rules with Z. Take a look at rule 3, which tells us that if W is selected, neither H nor Z is selected. That means
W —> ~H & ~Z
Taking the contrapositive of this, we get
H v Z —> ~W
OK, so now we know that if we pick Z, we can’t pick W. What else? Take a look at rule 4, which is related to W. It tells us that if M is selected, then W is also selected. In other words
M —> W
And the contrapositive of this is
~W —> ~M
We can combine these together to get H v Z —> ~W —> ~M
which means that if we pick Z, we can’t pick W, or M. So that gets rid of (B) and (C) automatically. Also, recall that M is a sapphire. That gets rid of (A) as well.
Is (D) possible? If we don’t pick any rubies, we have to just pick topazes and sapphires. But we already got rid of a topaz (W) and a sapphire (M). So that leaves us with 3 + 2 = 5 topazes and sapphires we could pick. But we need 6 stones, not 5, so we have to add a ruby to that, so (D) is impossible.
That just leaves (E), the correct answer. And if we pick all the rubies, and all the topazes except W, we see that none of the rules are violated.
Hope this helps! Feel free to ask any other questions that you might have.
