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Which of the following approaches do we use  to prove that  A ⊆ B ? {“version”:”1.1″,”math”:”\text{Which of the following approaches do we use }\\ \text{to prove that } A\subseteq B ?”}

The coefficient of x19y6 in the expansion of (x+y2)25 is {“version”:”1.1″,”math”:”\text{The coefficient of }x^{19}y^6 \text{ in the expansion of } (x+y^2)^{25} \text{ is } “}

Select all anti-symmetric relations.

Suppose a box contains 12 apples, 15 oranges and 20 pears. How many fruits do you have to pick from the box to guarantee that you have at least 12 oranges?

If a relation R on a set is a total ordering, then R must also be a partial ordering.

When proving the statement,  `if  x 3  is irrational then  x  is irrational’   using contradiction we assume that  x 3  is rational. {“version”:”1.1″,”math”:”\text{When proving the statement, } \\ \textbf{`if $x^3$ is irrational then $x$ is irrational’ }\\ \text{ using contradiction we assume that } x^3 \text{ is rational.}”} 

Consider the relation R defined on S, where S is the set of all cars, and R={(x,y) | x and y are red cars}. Select all true statements.

Consider the relation R on S, where S is the set of all people, and R={(G,H) | G and H have the same number of biological children}.  Select all true statements.

Suppose a group consists of five males and seven females. How many ways can you select a committee of four members from the group, if the committee is required to have at least two females?

1+1=3 if and only if sharks can walk.