# Using deductive logic

George, Sergio, Kim, Nicolas, Michael, Joan, and Orlando are welders. Four of these welders will be hired to seal the nuclear waste containers used at Hanford waste site. The four must pass a high-level security clearance in addition to passing a rigorous weld test.

The four are to be chosen according to the following conditions:

If George or Sergio passes the weld test, the other will pass; if either fails, they both fail.

If Nicolas or Kim passes the security clearance, the other will pass; if either fails, they both fail.

If Nicolas or Sergio passes the weld test, the other will pass, too.

If Michael or Joan fails the security clearance, the other will pass.

Orlando and George passed the security clearance.

Michael and Sergio passed the weld test.

Kim passed security clearance.

Orlando passed weld test.

Joan fails security clearance.

Which of the following could be a list of welders hired to seal nuclear containers?

Select one:

a. Nicolas, Sergio, Joan, Kim

b. Joan, Michael, Kim, Sergio

c. Michael, George, Nicolas, Orlando

d. Orlando, George, Michael, Sergio

Would the answer be C ?

• Hi, welcome to Philosophy SE. Please visit our Help Center to see what questions we answer and how to ask. We typically do not answer such HW questions, at least not unless you rephrase it to spell out the difficulty you are having. Commented Oct 24, 2017 at 0:28
• I wrote an answer, but realized, in this case, you could just test all 4 possible answers?
– user935
Commented Oct 25, 2017 at 19:09

This is a type of zebra puzzle, also known as Einstein's Puzzle or a logic grid puzzle

As noted in the page above, they can usually be solved using logic grids. Two website w/ more info:

Of course, since the puzzles involve basic prepositional logic, there are other ways to solve them as well. In particular, computer languages such as Prolog have been designed to solve problems like these without looking at all possible combinations of variables (the brute force method)

It seems that the answer could be either (c) or (d) with most evidence favoring (c).

Here is the main constraint:

The four must pass a high-level security clearance in addition to passing a rigorous weld test.

However, "Joan fails security clearance." Joan is in groups (a) and (b). So, groups, (a) and (b) are not selected.

Michael, George and Orlando are in the two remaining groups (c) and (d). Since it is given that four of the welders will be hired these three must have passed both the weld test and the security clearance otherwise no group would be selected.

That means we can focus on Nicolas in group (c) or Sergio in group (d). Do either of these fail the tests?

Nicolas passes the security clearance because Kim does. Nicolas and Sergio both pass the weld test. So Nicolas passes both the weld test and the security clearance. Group (c) has met all the requirements to be be selected.

Can we eliminate Sergio and in so doing say for sure that group (d) could not be selected? Sergio passed the welding test. Did he pass security clearance?

I don't see any way to tell if Sergio passed the security clearance or not. However, only one group will be selected. Since group (c) meets all the requirements, I would pick group (c).