Page 71 - computer science (868) class 11
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R = “There will be damage to life and property”
                       Write these statements in symbolic form.
                       i.  If there is a prediction for a cyclone, then it is raining heavily and there will be damage to life and property.
                      ii.  It is raining heavily and there is a prediction of a cyclone.
                      iii.  There is a prediction for a cyclone if and only if it is raining heavily.
                      iv.  It is not raining heavily or there is no prediction for a cyclone.
                       v.  If there is a prediction for a cyclone, then there will be damage to life and property.
                    3.  Consider the following propositions:
                       P  = “It is raining heavily”
                       Q = “There is a prediction for cyclone”
                       R  = “There will be damage of life and property”
                       Express the following statements in words.
                       i.  ∼P ∨ ∼Q
                      ii.  ∼P ∨ (∼Q ∧ ∼R)
                      iii.  ∼P ↔ ∼Q
                      iv.   ∼(P ∧ Q ∧ R)
                       v.   ∼Q → ∼R
                    4.  Write the converse, inverse and contrapositive for the following propositions:
                       i.  If you work hard, then you will crack IIT.
                      ii.  If the flower has a beautiful smell, then it is a rose.
                      iii.  If I am invited to a party, then I will wear my red gown.
                      iv.  If India wins World Cup cricket, then we will celebrate.
                       v.  If a number is equal to its reverse, then it is a palindrome.
                    5.  Construct a truth table and check if the following propositions are tautology, contradiction or contingency.
                       i.  (a) → (a ∧ b)
                      ii.  b → (∼a → b) ↔ a
                      iii.  (a ∧ b) → (∼a ∧ ∼b)
                      iv.  [(a → b) → (b → c)] → a
                       v.  (a ∧ 0) → (∼a ∧ b)
                      vi.  a ∧ (a → b) → b
                      vii.  (a ↔ b) ∧ (∼a ↔ ∼b)
                     viii.  (a ∧ b) → (∼a ∧ b) → (∼b ∧ a)
                      ix.  ∼(a ∨ b) ∧ (a ∨ b)
                      x.  ∼(a ∧ b ∧ c) ∨ (a ∧ b ∧ c)
                    6.  Complete the truth table given below:
                                          P        Q      P → Q    (P → Q) → P'    ∼((P → Q) → ∼P)








                    7.  Given the following logical circuit:

                                                                        ?1?
                                     A
                                                                                       ?3?
                                                                                                   ?4?
                                     B                                ?2?




                                     C





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                                                           Propositional Logic, Hardware Implementation, Arithmetic Operations  69
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