a) Define (using truth tables) the disjunction, conjunction, exclusive or, conditional, and biconditional of the propositions p and q.________________b) What are the disjunction, conjunction, exclusive or, conditional, and biconditional of the propositions "I'll go to the movies tonight" and "I'll finish my discrete mathematics homework"?

Solution a) Step 1 Definition Disjunction : A compound statement formed by joining two statements with the connector “OR” is called a disjunction .Symbol of “ “ is Truth table p r True True True True False True False True True False False FalseStep2 Conjunction : Conjunction is a compound statement formed by joining two statements with the connector “AND”.Symbol of “ “ is Truth Table p r True True True True False False False True False False False FalseStep 3Exclusive or:p , r are any two propositions . Exclusive or is represented as and its meaning is “either p or q but not both “.Truth table p r True True False True False True False True True False False FalseStep 4Conditional : p , r are any two propositions .Conditional is represented as And its meaning is “ if p then r “Truth table p r True True True True False False False True True False False TrueStep 5Biconditional p , r are given propositions and Biconditional represented as ,and its meaning is “ p if and only if r ”. p r True True True True False False False True False False False Trueb) Given propositions are “ I’ll go to the movies tonight “ and “I’ll finish my discrete mathematics homework”.Disjunction : I’ll go to the movies tonight or I’ll finish my discrete mathematics homework.Conjunction: I’ll go to the movies tonight and I’ll finish my discrete mathematics homework.Exclusive or: Either I’ll go to the movies tonight or I’ll finish my discrete mathematics homework.Conditional: If I’ll ’ll go to the movies tonight then i’ll finish my discrete mathematics homework Biconditional : I’ll go to the movies tonight if and only if I’ll finish my discrete mathematics homework.