   Chapter 1.7, Problem 16E

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# Let A = { 1 , 2 , 3 , 4 } and define R on ℘ ( A ) − { ϕ } by x R y if and only if x ∩ y ≠ ϕ . Determine whether R is reflexive, symmetric, or transitive.

To determine

Whether the given relation R on (A){ϕ} is reflexive, symmetric or transitive.

Explanation

Given Information:

(A){ϕ} is the set of all nonempty subsets of A={1,2,3,4} and a relation R on a nonempty set (A){ϕ} defined by xRy if and only if xyϕ.

Formula Used:

(1) A relation R on a nonempty set A is reflexive if the following property is satisfied:

xRx for all xA.

(2) A relation R on a nonempty set A is symmetric if the following property is satisfied:

If xRy, then yRx.

(3) A relation R on a nonempty set A is transitive if the following property is satisfied:

If xRy and yRz, then xRz.

Explanation:

Let x,y,z(A){ϕ}

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