EF Exercises

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Exercises 3.3 Exercises

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Creating truth tables.

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In each of Exercises 1–2, write out the truth table for the given boolean polynomial.

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1.

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p (x, y) = (x \land y)^{'} \land x^{'} .

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2.

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q (x, y, z) = (x \lor y)^{'} \land (z \lor x) \land y .

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3.

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Explain why the boolean polynomial

p (x, y) = x \lor y \lor y^{'}

is not in disjunctive form.

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Disjunctive normal form from a truth table.

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In each of Exercises 4–6, write out a boolean polynomial in disjunctive normal form that has the given truth table.

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4.

$x$	$y$	$p (x, y)$
$1$	$1$	$1$
$1$	$0$	$1$
$0$	$1$	$1$
$0$	$0$	$0$

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5.

$x$	$y$	$p (x, y)$
$1$	$1$	$1$
$1$	$0$	$0$
$0$	$1$	$1$
$0$	$0$	$0$

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6.

$x$	$y$	$z$	$p (x, y, z)$
$1$	$1$	$1$	$1$
$1$	$1$	$0$	$0$
$1$	$0$	$1$	$0$
$1$	$0$	$0$	$0$
$0$	$1$	$1$	$1$
$0$	$1$	$0$	$0$
$0$	$0$	$1$	$0$
$0$	$0$	$0$	$0$

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Disjunctive normal form from a boolean polynomial.

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In each of Exercises 7–9, write out a boolean polynomial in disjunctive normal form that is equivalent to the given boolean polynomial.

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7.

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p (x, y, z) = (x \lor y) \land z .

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8.

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q (x, y, z) = [(x \land y^{'}) \lor (x \land z)]^{'} \lor x^{'} .

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9.

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r (x, y, z) = (x \land y^{'}) \lor (x \land z) \lor (x \land y) .

Elementary Foundations: An introduction to topics in discrete mathematics

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Exercises 3.3 Exercises

Creating truth tables.

1.

2.

3.

Disjunctive normal form from a truth table.

4.

5.

6.

Disjunctive normal form from a boolean polynomial.

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9.