2. Let p and q be the propositions p: Smoke detector measurements are above the

Q: 2. Let p and q be the propositions p: Smoke detector measurements are above the

Signs: Meaning ^ : AND ~:NOT ->:LEADS TO a) Smoke detector above threshold leads to camera being ON i.e. p leads to q p -> q b) Here Smoke detector should be above threshold AND Camera detecting forest fire will lead to alarm being ON (p ^ r) -> s c)Here Smoke detector should be above threshold AND Camera doesn't detect forest fire will lead to alarm being OFF (p ^ ~r) -> ~s

ID: 3602050 • Letter: 2

Question

2. Let p and q be the propositions p: Smoke detector measurements are above the threshold q The camera is turned on. r: The camera detects forest fire. s: The alarm is turned on. Write these propositions a) If the smoke detector measurements are above threshold the camera is turned on. b) If the smoke detector measurements are above threshold and the camera detects forest fire then the alarm is turned orn. o If the smoke detector measurements are above the threshold but the camera does not detect forest fire, the alarm is not turned on.

Explanation / Answer

Signs: Meaning

^ : AND
~:NOT
->:LEADS TO

Smoke detector above threshold leads to camera being ON i.e. p leads to q

p -> q

b) Here Smoke detector should be above threshold AND Camera detecting forest fire will lead to alarm being ON

(p ^ r) -> s

c)Here Smoke detector should be above threshold AND Camera doesn't detect forest fire will lead to alarm being OFF

(p ^ ~r) -> ~s

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2. Let p and q be the propositions p: Smoke detector measurements are above the

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