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Use set builder notation to give a description of each of these sets. a) {0, 3, 6, 9, 12} b) {−3,−2,−1, 0, 1, 2, 3} c) {m, n, o, p}



Determine whether each of the following statements is a proposition or not. If it is, give its truth value.


Use a Venn diagram to illustrate the subset of even integers in the set of all positive integers not exceeding 15.


let a and b be sets. show that (a∩b)⊆a


  1. Show that ¬p → (q + r) and q→ (p V r) are logically equivalent.
  2. show, by the use of the truth table (truth matrix), that the (p v q)v[(p¬)ʌ(q)] is a contradiction.

Show that  p⟷q and (p∧ q) V (¬p ∧ ¬q) are logically equivalent.


  1. Show that are logically equivalent.
  1. Identify if the statement  is a tautology, contradiction, or contingency.
  2. Show that are logically equivalent.

{x/x is an integer such as x2 =2}


show in a truth table that p↔q and (p^q) v (¬p^¬q) are logically equivalent.