6.2.30 BINARY RELATIONS

Condition: for relations \ (\ alpha, \ beta, \ gamma \), set on the final set \ (a = \ {1.2,3,4,5,6,6 \} \), find \ [\ beta \ cdot \ gamma; \ gamma^{-1} \ cdot \ beta \ cdot \ alpha, \ text {if} \ alpha = \ left (\ begin {array} {lll} 3 & 4 & 2 \\ 4 & 1 & 6 & 6 & 6 & 6 & 6 & 6 & 6 & 6 & 6 & 6 & 6 & 6 & 6 & 6 & 6 & 6 \ end {Array} \ Right) \ Text {,} \] \ [\ BETA = \ LEFT (\ Begin {Array} {lll} 6 & 1 & 4 \\ 2 & 3 & 3 \ End {Array} \ Right), \ Quad \ Gamma = \ Left (\ Begin {Array} {lll} 6 & 1 \\ 2 & 3 & 3 \ end {Array} \ Right) \]