Page 18 - Computer science 868 Class 12
P. 18

The truth table for negation is given below considering ‘a’ as a proposition variable:

                                                            a          ∼a
                                                            0           1
                                                            1           0
              •  If a = “AR helps in learning” then ∼a = “AR does not help in learning”.
              •  If b = “Smart watches help in health management” then ∼b = “Smart watches do not help in health management”.

              1.3.2 Conjunction (AND)
              Conjunction is a binary connective as it joins two or more simple propositions. It results in true if all proposition
              variables are true. If any variable is false, the resulting output is false. It 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 = “Smart watches have a small battery life”
                  b = “Smart watches are costly”

              Then a ∧ b = “Smart watches have a small battery life and Smart watches are costly”.
              •  If x = “Jupiter is composed of hydrogen”.
                  y = “Jupiter is the largest planet in our Solar system”.

              Then x ∧ y = “Jupiter is composed of hydrogen and Jupiter is the largest planet of our Solar system”.

              1.3.3 Disjunction (OR)
              Disjunction 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. It is represented by + or ∨.

              The truth table using 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 = “Rani likes to wear dresses”.

                  b = “Rani likes to wear sarees”.
              Then a ∨ b = “Rani likes to wear dresses or Rani likes to wear sarees”.
              •  If m = “Raghav is preparing for engineering”.
                   n = “Raghav is preparing for medical”.

              Then m ∨ n = “Raghav is preparing for engineering or Raghav is preparing for medical”.







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