Consider the following statement, \"If switch B is pressed, then the camera focu
ID: 3141592 • Letter: C
Question
Consider the following statement, "If switch B is pressed, then the camera focus is on manual." Which of the following statements is logically equivalent? If switch B is pressed, then the camera focus is not on manual. If the camera focus is on manual, then switch B is pressed. If the camera focus is not on manual, then the switch B has not been pressed. Combine the conditional statement and its converse into a bi-conditional statement. If the student council is right, then the administration is wrong. If the administration is wrong, then the student council is right. Write the following bi-conditional statement as two separate statements -a conditional statement and its converse. The prisoners will be set free if and only if there are peace talks.Explanation / Answer
27: Let p: Switch B is pressed; q: The camera focus is on manual
Given: p -> q
We know by the law of contrapositive that this is equivalent to ~q -> ~p
which is
If the camera focus is not on manual, then switch B has not been pressed.
28. p: The student council is right; q: The administration is wrong.
Given p -> q and q -> p
Combining => p <-> q
which is
The student council is right if and only if the administration is wrong.
29. p: The prisoners will be set free; q: there are peace talks.
Given: p <-> q
This can be split as p -> q and q -> p
which are
If the prisoners will be set free then there are peace talks.
If there are peace talks then the prisoners will be set free.
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