Recent content by iHeartof12

(x,y)R(x,y) is true for all real x,y so the relation is reflexive. z+x≤w+y so (z,w)R(x,y) and the relation is symmetric. How would I show that the relation isn't transitive?

Indicate if the following relation on the given set is reflexive, symmetric, transitive on a given set. R where (x,y)R(z,w) iff x+z≤y+w on the set ℝxℝ. It is reflexive because any real number can make x+z=y+w. It is not symmetric because if x+z≤y+w it's not possible for x+z≥y+w. It is...

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Indicate which of the following relations on the given sets are reflexive on a given set, which are symmetric and which are transitive. {(x,y)\inZxZ: x+y=10} Tell me if I'm thinking about this correctly It is not reflexive because the only 5R5. It is symmetric because any xRy and yRx where...

Let A be a nonempty set. P is a partition of A iff P is a set of subsets of A such that i. if X \inP, then X ≠∅ ii. if X \inP and if Y \inP, then X=Y or X\capY=∅ iii. X\inP\bigcupX=A

For the given set A, determine whether P is a partition of A. A= ℝ, P=(-∞,-1)\cup[-1,1]\cup(1,∞) Is it correct to say that P is not partition? I don't understand why. Thank you

For the given set A, determine whether P is a partition of A. A= {1,2,3,4,5,6,7}, P={{1,3},{5,6},{2,4},{7}} Is it correct to say that P is a partition of A? Thank you

For the given set A, determine whether P is a partition of A. A= {1,2,3,4}, P={{1,2},{2,3},{3,4}} Is it correct to say that P is a partition of A? Thank you

Let A,B and C be sets. Prove that (A-B)-C=(A-C)-(B-C). Attempted solution: i. Suppose x \in (A-B)-C. Since x \in (A-B)-C this means that x \in A but x \notin B and x \notin C. ii. Suppose x \in (A-C)-(B-C). Since x \in (A-C)-(B-C) it makes since that x \in A and x \notin B and x...

Let A,B and C be sets. Prove that (A-B)-C=(A-C)-(B-C). Attempted solution: Suppose x \in (A-B)-C. Since x \in (A-B)-C this means that x \in A but x \notin B and x \notin C. I'm not sure how to show how these two statements are equal.

ok thank you for your help

Ok I think I get it tell me if I worded this correctly: Suppose x \in A and A \cap B = \emptyset Since x \in A and A \subset B \cup C, this means that x \in B or x \in C. Consequently, x cannot be in B, because if it were, then we would have x \in A \cap B = \emptyset, which is impossible...

Since A\bigcapB=∅, x\inA or x\inB. Thus x\inA, x\notinB and x\inC. Therefor A\subseteqC. Is that a good way to show how to exclude the possibility of x\inB?

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Let the universe be the set of Z. Let E, D, Z+, and Z- be the sets of all even, odd, positive, and negative integers respectively. Find ∅c. My thoughts were that since the universe is the set of all integers the ∅c would be all integers. Am I correct in my thinking or would the ∅c be...