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
Â
(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)
Â
(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)
Â
(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)Â
Solution:
(a) "p\\land \\lnot q:\\text{Kelly is at home and Hannah is not at home}"
"(p\\land q)\\land r: \\text{Kelly, Hannah and Sunny are at home}"
(b) Define "p: \\text{You should pay the fares for the tickets}"
"q:\\text{You plan to visit Northern Pakistan in winter}"
Then symbolically,
"p\\rightarrow q"
(c) Define "p: \\text{The lift in our office is installed }"
"q:\\text{One can use the lift}"
Converse: If we can use the lift , then the lift in our office is installed
Symbolically: "q\\rightarrow p"
(d) Define "p:\\text{We do not make a plan to plant marigold flowers}"
"q:\\text{It is nott suitable season for them}"
Contrapositive : If it is a suitable season, then we make a plan to plant marigold flowers
Symbolically: "q\\rightarrow p"
(e) Define "p:\\text{It is a right angled triangle}"
"q:\\text{Pythagoras rule applies }"
Biconditional : A triangle is a right angled triangle iff it satisfies Pythagoras rule
Symbolically: "p\\leftrightarrow q"
Comments
Leave a comment