1. All men are happy if there is a woman who likes them.
2. There is a woman who likes all men who are meateaters.
3. Ng is a meateater man.

From 1.

(1)

From 2.

(2)

(3)

From 3.

(4)

(5)

(4) + (3) {w/Ng}

(6)

(6) + (5) { }

(7)

(1) + (4) {x/Ng}

(8)

(8) + (5) {y/M}

(9)

(9) + (7) { }

Therefore Ng is happy.