Give a natural deduction proof from assumption ¬(φ → ψ) to conclusion φ ∧ ¬ψ.

The first floor of marcus’ house is 1,440 square feet. he will cover 1,033 square feet with wood and the rest with tile. a box of tiles will cover 11 square feet. how many boxes of tile does marcus need to buy to cover the floor?

Aclothing store has the sign shown in the shop window. pani sees the sign and wants to buy 3 shirts and 2 pairs of jeans. the cost of each shirt before the discount is $12, and the cost of each pair of jeans is $19 before the discount. write and simplify an expression to find the amount pani pays if a $3 discount is applied to her total

Asquare and an equilateral triangle have the same perimeter. each side the triangle is 4 inches longer than each side of the square. what is the perimeter of the square