Problem-50

Problem-50 Find the sum-of-products expansions of these Boolean functions. a) F(x,y,z)=x+y+z b) F(x,y,z)=(y+x)z c) F(x,y,z)=y d) F(x,y,z)=x   Solution a) F(x,y,z)=x+y+z   b) F(x,y,z)=(y+x)z   c) F(x,y,z)=y   d) F(x,y,z)=x  

Problem-48

Problem-48 Use a table to express the values of each of these Boolean functions. a) F(x,y,z)=  b) F(x,y,z)=y+xz c) F(x,y,z)=x +  d) F(x,y,z)=y(xz+ )   Solution a) F(x,y,z)=   x  y  z   1…

Problem-45

Problem-45 Let R1={(1,2),(2,3),(3,4)} and R2={(1,1),(1,2),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3),(3,4)} be relations from {1,2,3} to {1,2,3,4}. For the ordered pair (a,b), write the ordered pairs in increasing order of a and then b, separated by commas without any spaces. For example,…

Problem-44

Problem-44 For each of these relations on the set {1,2,3,4}, decide whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive. a) {(2,2),(2,3),(2,4),(3,2),(3,3),(3,4)}…

Problem-43

Problem-43 a) List all the ordered pairs in the relation R={(a,b)|adividesb} on the set {1,2,3,4,5,6}. Write the ordered pairs in increasing order of a and then b, separated by commas without…

Problem-42

Problem-42 Determine whether each of these functions is a bijection from R to R. a) f(x)= +1 b) f(x)=−5x+6 c) f(x)=− +7 d) f(x)=x+ +4   Solution   a) f(x)= +1   f    is  a bijection from  R to R.    b) f(x)=−5x+6…

Problem-41

  Problem-41 Determine whether f:Z×Z→Z is onto if a)  f(m,n)=m2−16 b)  f(m,n)=|m|−|n|. c) f(m,n)=m+n+6. d)  f(m,n)=4m−n. e) f(m,n)=m2−n2   Solution   a)  f(m,n)=m2−16 not onto   b)  f(m,n)=|m|−|n|. onto   c) f(m,n)=m+n+6. onto   d)  f(m,n)=4m−n. onto   e) f(m,n)=m2−n2 not…