Page 74 - Cs_withBlue_J_C11_Flipbook
P. 74

Definition
                    A truth table is a table which shows the truth values of all the possible combinations of inputs. It is used to find if a
                    compound statement is true or false.



                  3.3 CONNECTIVES
              Now,  we  know that connectives  or logical operators join  two or more  simple  propositions  to form a compound
              proposition. There are mainly five connectives which are as follows:
              •  Negation (NOT): It inverts a single statement. It is also called a unary connective. If a proposition is true, negation
                 makes it false and vice versa. Negation is represented by ˜(tilde) or ‘ (apostrophe) or   ̅ (bar).
                The truth table for negation is given below considering ‘a’ as a propositional variable:
                                                          a              ∼a
                                                          0              1

                                                          1              0
                   If a = “It is raining heavily” then ∼a = “It is not raining heavily.”
                   If b = “Planet X is the ninth planet” then ∼b = “Planet X is not the ninth planet.”
              •  Conjunction (AND): It is a binary connective as it joins two or more simple propositions. It results in true if all
                 propositional variables are true. If any variable is false, the resulting output is false. A conjunction is represented by
                 a dot (.) or (∧). The truth table for conjunction using two variables ‘a’ and ‘b’ is given below:

                                                     a            b          a ∧ b
                                                     0            0            0
                                                     0            1            0
                                                     1            0            0
                                                     1            1            1

                   If a = “10 is an even number.”
                      b = “10 is divisible by 5.”
                  Then, a ∧ b = “10 is an even number and 10 is divisible by 5.”
                   If x = “Light is a form of energy.”
                      y = “Light travels in a straight line.”
                  Then, x ∧ y = “Light is a form of energy and light travels in a straight line.”
              •  Disjunction (OR): It is also a binary connective that results in true if any one proposition is true. The output is false
                 only when both propositions are false. A disjunction is represented by a plus (+) or (∨).
                The truth table for disjunction using two variables ‘a’ and ‘b’ is given below:

                                                     a            b          a ∨ b
                                                     0            0            0
                                                     0            1            1
                                                     1            0            1
                                                     1            1            1

                   If a = “Raj is wearing a blue jersey.”
                      b = “Raj is wearing a red jersey.”
                  Then a ∨ b = “Raj is wearing a blue jersey or Raj is wearing a red jersey.”




                7272  Touchpad Computer Science-XI
   69   70   71   72   73   74   75   76   77   78   79