Month: March 2014

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 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…

Problem-40 Determine whether the following function from {a,b,c,d} to itself is one-to-one. f(a)=b,f(b)=c,f(c)=d,f(d)=c   Solution This is not one-to-one .

Problem-39 Find these values. a) ⌊1.7⌋ b) ⌈1.7⌉ c) ⌊−9.8⌋ d) ⌈−9.8⌉ e) ⌈2.96⌉ f) ⌈−2.96⌉ g) ⌊+⌈⌉⌋ h) ⌈⌊⌋+⌈⌉+⌉   Solution   a) ⌊1.7⌋ 1 b) ⌈1.7⌉ 2 c)…

Problem-37 Why is f not a function from R to R if a) f(x)= ? b) f(x)=±   ?   Solution a) f(x)= ? f(0) is not defined.   b) f(x)=±  ? f(x) is not well-defined because there…

Problem-36 The symmetric difference of A and B, denoted by A⊕B, is the set containing those elements in either A or B, but not in both A and B. Find…

Problem-35 Select the correct Venn diagram for each of these combinations of the sets A, B, and C. a) A∪(B∩C) b) c) (B−A)∪(C−B)∪(A−C)   Solution a) A∪(B∩C) b)   c) (B−A)∪(C−B)∪(A−C)  

Problem-34 Find the sets A and B if A−B={1,5,6,8}, B−A={0,10}, and A∩B={3,7,9}.   Solution A={1,3,5,6,7,8,9},B={0,3,7,9,10}  

Problem-33 Let A={a,b,c,d,e} and B={a,b,c,d,e,f,g,h}. Find a) A∩B b) A−B   Solution a) A∩B {a, b, c, d, e}   b) A−B {}