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Q43E

Expert-verifiedFound in: Page 35

Book edition
7th

Author(s)
Kenneth H. Rosen

Pages
808 pages

ISBN
9780073383095

**Show that, ${\mathbf{\wedge}}{\mathbf{,}}{\mathbf{\vee}}$and$\mathbf{\neg}$, ****∨****form a functionally complete collection of logical operators. [Hint: Use the fact that every compound proposition is logically equivalent to one in disjunctive normal form, as shown in Exercise 42.] **

Let P be a compound proposition. Generate a proposition q in disjunctive normal form, which is equivalent to p.

Let p be a compound proposition.

We can generate its truth table, and according to the preceding exercise (42),

Generate a proposition q in disjunctive normal form, which is equivalent to p.

The disjunctive normal form involves, $\neg ,\vee $and $\wedge $only, which proves the statement,

given the definition of functionally complete collection of operators.

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