Question

Find the dual of each of these compound propositions. b) (p /\ q/\ r) v s

Answer 1

Answer: (p ∨q∨r)∧s

Explanation:

Our proposition is:

(p /\ q/\ r) v s

This means

(P and Q and R ) or S

The proposition is true if P, Q and R are true, or if S is true.

Then the dual of this is

(P or Q or R) and S

The dual of a porposition can be obtained by changing the ∧ for ∨, the ∨ for ∧, the Trues for Falses and the Falses for Trues.

Then, the dual can be writted as:

(p ∨q∨r)∧s

The proposition is true if S is true, and P or Q or R are true.

Answer 2

`(p\lor q \lor r)\land s`

Explanation:

The dual of a compound preposition is obtained by replacing

`\land \;with\;\lor`

`\lor \;with\;\land`

and replacing T(true) with F(false) and F with T.

So, the dual of the compound proposition

`(p\land q \land r)\lor s`

is

`(p\lor q \lor r)\land s`