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-49
Problem-49 Find a Boolean product of the Boolean variables x, y, and z, or their complements, that has the value 1 if and only if x=1,y=0, and z=1. Solution …
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-47
Problem-47 Find the values, if any, of the Boolean variable x that satisfy these equations. a) x⋅1=0 b) x+x=0 c) x⋅1=x d) x.=1 Solution a) x⋅1=0 x=0 b) x+x=0…
Problem-46
Problem-46 Find the values of these experssions. a) 0. b) 1+ c) .1 d) Solution a) 0. 0 b) 1+ 1 c) .1 0 d) 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…
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