Ignore what they are calling it and draw a truth table for what they describe. There appears three inputs: "the current state" which you can arbitrarily call Q(n), N, and M. There is one output which we can arbitrarily call Q(n+1). The names are not totally arbitrary, because Q(n+1) is by definition a one-time-step delayed version of Q(n) (i.e. Q(n) is the previous output).
Inputs Outputs
Q(n) M N Q(n+1)
0 0 0 ?
0 0 1 ?
0 1 0 ?
0 1 1 ?
1 0 0 ?
1 0 1 ?
1 1 0 ?
1 1 1 ?
You should be able to fill in the question marks from the narrative description trivially. This is a truth table.
I believe an excitation table is just a rephrasing of the truth table where the valid entries are include 0, 1, and Q(n) and it's complement /Q(n) (so there are only two "real" inputs). And removing "redundant" rows (i.e. if a variable is a don't-care under some conditions, then express that collapsed row with an "x" for that variable).
Inputs Outputs
M N Q(n+1)
0 0 Q(n), /Q(n), 0, or 1?
0 1 Q(n), /Q(n), 0, or 1?
1 0 Q(n), /Q(n), 0, or 1?
1 1 Q(n), /Q(n), 0, or 1?
Can you reduce this further once you put answers in to the question marks?
The first one is not master-slave; you would have to cascade two copies of that circuit (with the clock inverted between them) to get the same functionality as the second circuit, which is indeed a master-slave (edge-triggered) flip-flop.
Best Answer
Start with the original equation:
Y = K'J'Q + K'J + KJQ'
The trick is to create two terms that are equivalent to the middle term, using the fact that X + X' = 1:
Y = J'K'Q + JK'(Q + Q') + JKQ'
Y = J'K'Q + JK'Q + JK'Q' + JKQ'
Now factor the pairs of terms:
Y = K'Q(J + J') + JQ'(K + K')
Simplify, again using the fact that X + X' = 1:
Y = K'Q + JQ'
This is really obvious if you draw the Karnaugh map for the function. The JK' term is redundant, given the other two terms.