Express the negations of these propositions using quan- tifiers, and in english. a) every student in this class likes mathematics. b) there is a student in this class who has never seen a computer. c) there is a student in this class who has taken every mathematics course offered at this school. d) there is a student in this class who has been in at least one room of every building on campus

Efficient homemakers ltd. makes canvas wallets and leather wallets as part of a money-making project. for the canvas wallets, they need two yards of canvas and two yards of leather. for the leather wallets, they need four yards of leather and three yards of canvas. their production unit has purchased 44 yards of leather and 40 yards of canvas. let x be the number of leather wallets and y be the number of canvas wallets. draw the graph showing the feasible region to represent the number of the leather and canvas wallets that can be produced.