Statements with nested quantifiers: variables with different domains. the domain for the first input variable to predicate t is a set of students at a university. the domain for the second input variable to predicate t is the set of math classes offered at that university. the predicate t(x, y) indicates that student x has taken class y. sam is a student at the university and math 101 is one of the courses offered at the university. give a logical expression for each sentence. (a) sam has taken math 101.(b) every student has taken at least one math class.(c) every student has taken at least one class besides math 101. (d) there is a student who has taken every math class besides math 101. (e) everyone besides sam has taken at least two different math classes. (f) sam has taken exactly two math classes.

i think there was a typo. you wrote pat brings 3 quarts of ice-cream to the party. each serving of ice-cream is 1 6 quart. how many total servings of ice-cream does pat bring to the party? i think the bold is supposed to be 1/6. so 1 quart of ice cream = 6 servings. 6 * 3 = 18.

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)

2,160 π

step-by-step explanation: