title: Elements of Logic via Numbers and Sets (Springer Undergraduate Mathematics Series)
author:  D.L. Johnson 
description: From the reviews: It took me a while to appreciate the need for a course intended to introduce mathematics undergraduates to advanced mathematics after they finish the calculus sequence.  This was the first book I found that seems really close to the core. It is well-written and very well suited to such a course. (James M. Cargal, UMAP Journal, Vol. 31 (1), 2010)
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  1
  Sets
  TOPIC Ć
  Sets, Types of Sets, Disjoint Sets, 
  Complementary Sets, Subsets, 
  Power Set, Cardinal Number of 
  Sets, Operations on Sets
  1.
  Set A has m elements and set B has n elements. If the total
  number of subsets of A is 112 more than the total number
  of subsets of B, then the value of m×n is ______.
  [Sep. 06, 2020 (I)]
  2.
  Let S = {1, 2, 3, ... , 100}. The number of non-empty subsets
  A of S such that the product of elements in A is even is :
  [Jan. 12, 2019 (I)]
  (a)
  100
  2
  1
  -
  (b)
  (
  )
  50
  50
  2
  2
  1
  -
  (c) 250 – 1
  (d) 250 + 1
  3.
  Let S
  {x
  R : x
  0
  =
  Î
  ³
   and
  2|
  x
  3|
  x( x
  6)
  6
  0
  -
  +
  -
  +
  =
  . Then S :
  [2018]
  (a) contains exactly one element.
  (b) contains exactly two elements.
  (c) contains exactly four elements.
  (d) is an empty set.
  4.
  If f(x) + 
  1
  2f
  3x
  x
  æ
  ö =
  ç
  ÷
  è
  ø
  , x ¹ 0 and
  S = {x Î R : f(x) =