a) Suppose p, q and r mean “Kelly is at home, Hannah is at home and Sunny is at home then interpret the meaning of the statement p ∧∼q and (p ∧ q) ∧ r (b) You should pay the fares for tickets only if you plan to visit northern Pakistan in this winter. (Convert the sentence in symbolic notation) (c) If the lift in our office install then one can use the lift (write a converse of the statement in symbolic notation as well as a statement) (d) If we do not make a plan to plant marigold flowers then it is not suitable season for them. (Write the contrapositive statement in symbolic as well as a statement) (e) If it is right angled triangle then Pythagoras rule applies. (Convert the statements in biconditional statement in symbolic as well as a statement)
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Solution:
(a)
(b) Define
Then symbolically,
(c) Define
Converse: If we can use the lift , then the lift in our office is installed
Symbolically:
(d) Define
Contrapositive : If it is a suitable season, then we make a plan to plant marigold flowers
Symbolically:
(e) Define
Biconditional : A triangle is a right angled triangle iff it satisfies Pythagoras rule
Symbolically: