Write an informal negation for each of the following statements. Be careful to avoid negations that are ambiguous. (a) a.All dogs are friendly. b.All dogs are unfriendly. c.Not all dogs are unfriendly.    d. Some dogs are friendly e.There is at least one unfriendly dog. f.There is at least one friendly dog. (b) All graphs are connected.   a.All graphs are disconnected. b.Not all graphs are disconnected.     c.Some graphs are connected. d.There is at least one graph that is disconnected. e.There is at least one graph that is connected. (c) Some suspicions were substantiated.   a.All suspicions were substantiated. b.All suspicions were unsubstantiated.    c. Some suspicions were unsubstantiated. d.There is at least one suspicion that was unsubstantiated. e.There is at least one suspicion that was substantiated. (d) Some estimates are accurate. a.All estimates are accurate b.All estimates are inaccurate.    c. Some estimates are inaccurate. d.There is at least one estimate that is inaccurate. e.There is at least one estimate that is accurate.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Write an informal negation for each of the following statements. Be careful to avoid negations that are ambiguous.

(a)

a.All dogs are friendly.
b.All dogs are unfriendly.
c.Not all dogs are unfriendly.   
d. Some dogs are friendly
e.There is at least one unfriendly dog.
f.There is at least one friendly dog.

(b)

All graphs are connected.
 
a.All graphs are disconnected.
b.Not all graphs are disconnected.   
 c.Some graphs are connected.
d.There is at least one graph that is disconnected.
e.There is at least one graph that is connected.

(c)

Some suspicions were substantiated.
 
a.All suspicions were substantiated.
b.All suspicions were unsubstantiated.   
c. Some suspicions were unsubstantiated.
d.There is at least one suspicion that was unsubstantiated.
e.There is at least one suspicion that was substantiated.

(d)

Some estimates are accurate.
a.All estimates are accurate
b.All estimates are inaccurate.   
c. Some estimates are inaccurate.
d.There is at least one estimate that is inaccurate.
e.There is at least one estimate that is accurate.
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