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Review of Ch. 3—Matrices end of section 3.8

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

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Review of Ch. 3—Matrices end of section 3.8

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

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

  3. Ex Ex. V = ^ =

  4. Boolean product – notation: dot in a circle Let A=[aij] be an mxk 0-1 matrix and B=[bij] be a kxn 0-1 matrix Boolean product  notation: dot in a circle A  B = [cij] is an mxn matrix with cij=(ai1 ^ b1j) v (ai2 ^ b2j) v … v (aik^ bkj) note: ai1 comes from the ith row of A b1j comes from the jth column of B

  5. Boolean product A B = [cij]  cij=(ai1 ^ b1j) v (ai2 ^ b2j) v … v (aik^ bkj)  = Note: in answer, the 3rd row, 1st column comes from 3rd row of A, 1st column of B

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