Logical form and Equivalence

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Last updated 12:47 AM on 9/5/25
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25 Terms

1
New cards

Is 'The moon has craters' a statement?

Yes, it’s a statement (true).

2
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Is 'Please close the book' a statement?

No, it’s a command, not a statement.

3
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Is 'x – 5 = 10' a statement?

No, it depends on the value of x (not a statement until x is given).

4
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Is 'What is your favorite color?' a statement?

No, it’s a question, not a statement.

5
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Is '2 + 2 = 5' a statement?

Yes, it’s a statement (false, but still a statement).

6
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Translate 'I am neither tired nor hungry' (p = tired, q = hungry).

¬p ∧ ¬q.

7
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Translate 'It is not the case that I am tired, and it is not the case that I am hungry.'

¬p ∧ ¬q.

8
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Translate 'I am not tired but I am not hungry.'

¬p ∧ ¬q.

9
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Translate '0 < x < 4' (p = 0 < x, q = x < 4, r = x = 4).

p ∧ q.

10
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Translate 'x ≤ 4.'

q ∨ r.

11
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Translate '0 < x ≤ 4.'

p ∧ (q ∨ r).

12
New cards

Is 'The moon has craters' a statement?

Yes, it’s a statement (true).

13
New cards

Is 'Please close the book' a statement?

No, it’s a command, not a statement.

14
New cards

Is 'x – 5 = 10' a statement?

No, it depends on the value of x (not a statement until x is given).

15
New cards

Is 'What is your favorite color?' a statement?

No, it’s a question, not a statement.

16
New cards

Is '2 + 2 = 5' a statement?

Yes, it’s a statement (false, but still a statement).

17
New cards

Translate 'I am neither tired nor hungry' (p = tired, q = hungry).

¬p ∧ ¬q.

18
New cards

Translate 'It is not the case that I am tired, and it is not the case that I am hungry.'

¬p ∧ ¬q.

19
New cards

Translate 'I am not tired but I am not hungry.'

¬p ∧ ¬q.

20
New cards

Translate '0 < x < 4' (p = 0 < x, q = x < 4, r = x = 4).

p ∧ q.

21
New cards

Translate 'x ≤ 4.'

q ∨ r.

22
New cards

Translate '0 < x ≤ 4.'

p ∧ (q ∨ r).

23
New cards

Is 'Stop running!' a statement?

No, it’s a command.

24
New cards

Translate 'I am tired or I am hungry' (p = tired, q = hungry).

p ∨ q.

25
New cards

Translate 'If I am tired, then I am hungry' (p = tired, q = hungry).

p → q.