Answer to Question #123538 in Discrete Mathematics for Muhammad Hasnain

Question

Part (a): Determine whether the statement p→(q∨r) is equivalent to (p∧∼r)→q ?

Part (b): A survey team in Food Street is surveying of liking and disliking of people there. The food items to be considered in survey are of three types, Traditional heavy meals, Fast food, Dairy Products.

Draw Venn diagram and shade the areas separately which represent the following information
1.Traditional and Fast food liker but not Dairy product
2.Fast food or Dairy but not traditional
3.Dairy products and Traditional.

Answer 1

Truth table for p->(qV r) is follows:

p q r qVr p-> (qVr)

F F F F T

F F T T T

F T F T T

F T T T T

T F F F F

T F T T T

T T F T T

T T T T T

Truth table for (p∧∼r)→q

p q r (p∧∼r)→q

F F F T

F F T T

F T F T

F T T T

T F F F

T F T T

T T F T

T T T T

Hence both truth tables gives same output. Hence they are equal.

Below is the venn diagram given for each case.

t- Traditional

D- Diary

F- fastfood