5.12. Prove and interpret the given relations: a. ax:n E, ãx+17 A, na x | b. „Ez. |
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- For T:P5P3 and nullity(T)=4, find rank(T).Prove this is an equivalece relation. x related to y iff x2 - y2 is evenOur universe U is Z (integers), and R is the relation defined by R(x,y):=x<y^2 For example, R(3,-2) and R(1,1) are T, while R(5,-2) and R(3,1) are both F. R is relexive, symmetric, transitive? give counterexample
- Define a relation C from R to R as follows: For any (x, y) ∈ R x R, (x, y) ∈ C means that x² + y² = 4. Is (0, 2) ∈ C?Let R be a relation from A={−1,0,1,2} to B={a,n,i} such that (x,y) provided that x is non-negative and y is a vowel. Is R a function? If R is not a function which conditions/s is violated?Suppose x, n ∈ N and n not equal to 0. Then, show that xnis positive if and only if x is positive.