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Review of Ch. 3—Matrices end of section 3.8 This material is a prereq for the second half of ch. 8 on relations

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Let A=[a ij ] and B=[b ij ] be mxn zero-one matrices. Join AvB=[a ij v b ij ] where a v b = {1 if a=1 or b=1 {0 otherwise MeetA^B=[a ij ^ b ij ] where a ^ b={1 if a=b=1 {0 otherwise

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Ex Ex. V = ^ =

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Boolean product – notation: dot in a circle Let A=[a ij ] be an mxk 0-1 matrix and B=[b ij ] be a kxn 0-1 matrix Boolean product notation: dot in a circle A B = [c ij ] is an mxn matrix with c ij =(a i1 ^ b 1j ) v (a i2 ^ b 2j ) v … v (a ik ^ b kj ) note: ai1 comes from the ith row of A b1j comes from the jth column of B

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Boolean product A B = [c ij ] c ij =(a i1 ^ b 1j ) v (a i2 ^ b 2j ) v … v (a ik ^ b kj ) = Note: in answer, the 3 rd row, 1 st column comes from 3 rd row of A, 1 st column of B

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Representing Relations Rosen 7.3. Using Matrices For finite sets we can use zero-one matrices. Elements of each set A and B must be listed in some particular.

Representing Relations Rosen 7.3. Using Matrices For finite sets we can use zero-one matrices. Elements of each set A and B must be listed in some particular.

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