1. Determine if the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive where (x,y) R if and only if x = 1.
2. Find the Boolean product of the two matrices:
[ 0 1 0 ] [ 0 1 0 ]
[ 1 1 1 ] [ 0 1 1 ]
[ 1 0 0 ] [ 1 1 1 ]
a. Reflexive means (x,x) E R for all real number x. However, (2,2) is not E R since the first coordinate 2 is not = 1. R is not reflexive.
b. Symmetry means (x,y) E R implies (y,x) E R. However, (1,2) E R but (2,1) is not E R is not symmetric.
c. Antisymmetric means (x,y) E R and x is not = y ...
This solution defines what it means if a product is said to be reflexive, symmetric/antisymmetric, transitive or Boolean. It then shows how to find if a given relation is reflexive, symmetric, antisymmetric, or transitive and explains the logic behind the answer, then shows how to find the Boolean product of two matrices.