Let
For every
- Draw arrow diagrams for R, S, and T.
- Indicate whether any of the relations R, S, and T are functions.
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Chapter 1 Solutions
Discrete Mathematics With Applications
- Does the relation is a brother of have a reflexive property consider one male? A symmetric property consider two males? A transitive property consider three males?arrow_forwardLet and be lines in a plane. Decide in each case whether or not is an equivalence relation, and justify your decisions. if and only ifand are parallel. if and only ifand are perpendicular.arrow_forwardLet A = {1, 2, 3, 4], B = {a, b, c}, C = {x, y, z}. Consider the relations R from A to B and S from B to C as follows: R = {(1, b), (3, a), (3, b), (4, c)} and S = {(a, y), (c, x), (a, z)} (i) Draw the diagrams of R and S. (ii) Find the matrix of each relation R, S (composition) RoS. (iii) Write R −1 and the composition RoS as sets of ordered pairs. (b) Find x and y where: (i) (x + 2, 4) = (5, 2x + y); (ii) (y − 2, 2x + 1) = (x − 1, y + 2)arrow_forward
- Let A = {2, 4} and B = {1, 3, 5} and define relations U, V, and W from A to B as follows. For every (x, y) ∈ A ✕ B, (x, y) ∈ U means that y − x > 2, (x, y) ∈ V means that y − 1 = x 2 , and W = (2, 5), (4, 1), (2, 3) . Indicate whether any of the relations U, V, and W are functions. (Select all that apply.) U is a function.V is a function.W is a function.None of the relations are functions.arrow_forwardLet X = {a,b,c} and Y = {1,2,3,4}. Which of the relations A,B,C defined below are functions from X to Y? a.) A = {(a,1), (b,2), (c,3)}arrow_forward2. Let A = {1,2, 3, 4}, B = {a, ß, 7}, C = {x, y, z}. Consider the relations R from A to B and S from B to C as follows: R = {(1,8), (3, a), (3, 3), (4, 7)} and S = = {(a, y), (7, x), (a, z)} Find the following relations (a) Draw the diagrams of R and S. (b) Determine Ro S. (c) Find the matrix of each relation R, S and Ro S (d) Write R-1 and Ro S as sets of ordered pairs.arrow_forward
- 3. Let A = {-1, –3, – 5}, B = {a, B, 7}, C = {x, y, z}. Consider the relations R from A to B and S from B to C respectively. R = {(-1,8), (–3, a), (–3, 7)} and S = {(a, y), (B, x), (7, y), (y, 2)} Find the following relations (a) Find the composition Ro S. (b) Find the matrices MR, Ms and MRos of the respective relations R, S and Ro S. (c) Compare M Ros to the product MRMS.arrow_forwardLet A={1,2,3,4} and B={1,3,5} and define relation R from A to B as follows: For all (x,y) an element of A x B, (x,y) an element of R means that (y+x)/2 ∈ Z. a.) Find A x B b.) IS 2R3, 3R3, 2R5? c.) Draw the arrow diagram of the given relation d.) Is the relation a Function?arrow_forwardLet A = {4, 5, 6} and B = {5, 6, 7} and define relations R,S, and T from A to B as follows:For all (x, y) ∈ A × B,(x, y) ∈ R means that x ≥ y.(x, y) ∈ S means that x − y2 is an integer.T = {(4, 7), (6, 5), (6, 7)}.a. Draw arrow diagrams for R, S, and T .b. Indicate whether any of the relations R, S, and T arefunctions.arrow_forward
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