The NOT Operation

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Show your work for each problem.

1.
If $P$ is true, what is $\neg P$ ?
1. a)False
2. b)True
3. c)Both true and false
4. d)It depends on Q
2.
With 1 for true and 0 for false, what is NOT 1? Type 1 or 0.
3.
Which sentence is the negation of "Tom likes football"?
1. a)Tom likes football a lot
2. b)Tom hates football
3. c)Tom likes basketball
4. d)Tom does not like football
4.
What is $\neg(\neg 1)$ ? Type 1 or 0 (1 = true, 0 = false).
5.
Let P = " $4 + 4 = 8$ ". Find the value of P and of $\neg P$ , using 1 for true and 0 for false.
6.
Use the trick $\neg P = 1 - P$ to compute NOT 0 and NOT 1.
7.
What is the negation of "All birds can fly"?
1. a)Some birds can fly
2. b)All birds are unable to fly
3. c)Not all birds can fly
4. d)No bird can fly
8.
P = 0 and Q = 0. What is $\neg P \vee Q$ ? Type 1 or 0 (1 = true, 0 = false).
9.
The negation of " $x > 5$ " is:
1. a) $x \geq 5$
2. b) $x \leq 5$
3. c) $x \neq 5$
4. d) $x < 5$
10.
P = 1 and Q = 0. Evaluate $\neg(P \land Q)$ , then compare it with $\neg P \land Q$ (1 = true, 0 = false).
11.
P = "10 is divisible by 3" and Q = "10 is even". Evaluate $\neg P \land Q$ (1 = true, 0 = false).
12.
What is $\neg\neg\neg 0$ (three NOTs in a row)? Type 1 or 0 (1 = true, 0 = false).
13.
Let S = "Mia speaks French", and S is true. What is the value of the sentence "It is not true that Mia does not speak French"? Use 1 for true and 0 for false.
14.
Which expression always has the same value as $\neg(P \vee Q)$ ?
1. a) $\neg P \land \neg Q$
2. b) $\neg P \vee \neg Q$
3. c) $\neg P \vee Q$
4. d) $P \land Q$
15.
P = 1, Q = 0 and R = 1. What is $\neg(P \land \neg Q) \vee \neg R$ ? Type 1 or 0 (1 = true, 0 = false).
16.
P = 1 and Q = 0. Compute $\neg(P \land Q)$ and $\neg P \vee \neg Q$ and check that they are equal (De Morgan).
17.
With 1 and 0, AND is multiplication and NOT P is $1 - P$ . Compute NOT (1 AND 0) as $1 - 1 \times 0$ , then check the result with $\neg 1 \vee \neg 0$ .
18.
A garden sprinkler runs when $\neg R \land \neg W$ is true, where R = "it is raining" and W = "the soil is already wet". By De Morgan this is the same as $\neg(R \vee W)$ . Today R = 0 and W = 1. Does the sprinkler run? Use 1 for yes (true) and 0 for no (false).