2. + -11 points epp discmath5 6.3.024. let a = {t, u, v, w}, and let s, be the set of all subsets of a that do not contain w, and s, the set of all subsets of a that contain w. (a) find s. (enter your answer in roster notation. enter empty or for the empty set.) (b) find s, (enter your answer in roster notation. enter empty or o for the empty set.) (c) are s, and s, disjoint? yes o no (d) compare the sizes of s1 and 52: sy has elements, sz has elements, therefore the size of s the size of s2 -- is greater than is less than is equal to (e) how many elements are in s, usz? (f) what is the relation between su s2 and p(a)? os, u sy is not a subset of p(a) p(a) is not a subset of s, us2 o su s2 is a proper subset of p(a) op(a) is a proper subset of sus2 su s2 is equal to p(a)

In δabc shown below, ∠bac is congruent to ∠bca: triangle abc, where angles a and c are congruent given: base ∠bac and ∠acb are congruent. prove: δabc is an isosceles triangle. when completed (fill in the blanks), the following paragraph proves that line segment ab is congruent to line segment bc making δabc an isosceles triangle. (4 points) construct a perpendicular bisector from point b to line segment ac . label the point of intersection between this perpendicular bisector and line segment ac as point d: m∠bda and m∠bdc is 90° by the definition of a perpendicular bisector. ∠bda is congruent to ∠bdc by the definition of congruent angles. line segment ad is congruent to line segment dc by by the definition of a perpendicular bisector. δbad is congruent to δbcd by the line segment ab is congruent to line segment bc because consequently, δabc is isosceles by definition of an isosceles triangle. 1. corresponding parts of congruent triangles are congruent (cpctc) 2. the definition of a perpendicular bisector 1. the definition of a perpendicular bisector 2. the definition of congruent angles 1. the definition of congruent angles 2. the definition of a perpendicular bisector 1. angle-side-angle (asa) postulate 2. corresponding parts of congruent triangles are congruent (cpctc)