The domain of discourse is sets. Suppose some predicate Q is true for all elemenst of A: ∀a ∈ A Q(a). Recall the definition of subset: X ⊆ Y is defined as ∀b ∈ X b ∈ Y . Suppose B ⊆ A and C ⊆ B. Prove that ∀c ∈ C Q(c)

Divide: 1573 ÷ 7 = a) 222 r5 b) 223 r6 c) 224 r5 d) 224 r3

Use the following statements to write a compound statement for the conjunction or disjunction. then find its truth value. p: an isosceles triangle has two congruent sides. q: a right angle measures 90° r: four points are always coplanar. s: a decagon has 12 sides. a) a right angle measures 90° or an isosceles triangle has two congruent sides; true. b) a right angle measures 90° and an isosceles triangle has two congruent sides; true. c) a right angle measures 90° and an isosceles triangle does not have two congruent sides; false. d) a right angle measures 90° or an isosceles triangle does not have two congruent sides; true.

In the diagram, a building cast a 35-ft shadow and a flagpole casts an 8-ft shadow. if the the flagpole is 18 ft tall, how tall is the building? round the the nearest tenth.