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Exercises · Q5

Q.Find the component statements of the following compound statements and check whether they are true or false.

(i) Number 3 is prime or it is odd.
(ii) All integers are positive or negative.
(iii) 100 is divisible by 3, 11 and 5.
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  1. "Number 3 is prime or it is odd." p: 3 is prime (True). q: 3 is odd (True). Connective: or. T∨T=T \vee T= True.
  2. "All integers are positive or negative." p: All integers are positive (False — e.g., −5 is negative). q: All integers are negative (False — e.g., 5 is positive). Connective: or. F∨F=F \vee F= False. (Note: 0 is itself neither positive nor negative, an additional reason both components fail.)
  3. "100 is divisible by 3, 11 and 5." …

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