ask 3 ========= Subtask b ------------ - Let ? be the set {true, false}. Then one can define the logical connectives ∨, ∧, →, ↔ as functions over the sets ? × ? → ? (taking in two arguments from the set ?, and returning an element from the set ?). It will then be an error if you try to give the functions something other than Boolean values. - You come to the right conclusion, but I think you have misunderstood the statement. Subtask b ------------ - Looks like you've reversed the numerator and denominator. - You don't really convince me with your argument. Can you see
Task 3 ========= Subtask b ------------ - Let ? be the set {true, false}. Then one can define the logical connectives ∨, ∧, →, ↔ as functions over the sets ? × ? → ? (taking in two arguments from the set ?, and returning an element from the set ?). It will then be an error if you try to give the functions something other than Boolean values. - You come to the right conclusion, but I think you have misunderstood the statement. Subtask b ------------ - Looks like you've reversed the numerator and denominator. - You don't really convince me with your argument. Can you see how you can make it clearer?
![Question 3
For each of the following statements, write the statement as a logical formula, say if it is true or not, and then prove or disprove the statement.
(a.) "for all prime numbers p greater than 2, it is the case that (p+2) or (p+4) is also a prime number"
(b.) "for all odd natural numbers n, it is the case that n²-1 is divisible by 4"
State clearly what you try to establish in your argument, and why your argument proves or disproves the statement.
(For examples on how to write down proofs, please look at Proof Methods and/or Extra Exercises on Predicate Logic.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4dad2a6e-2152-43f0-a66f-03d554c1bef7%2F13b86075-25be-433d-b9be-9780d4589e8e%2Fyj2069_processed.png&w=3840&q=75)
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Here, in the question, we have to write the statements as a logical formula and also say if it is true or not, and then prove it or disprove it. We shall have a clear understanding of the concept of the odd number, prime numbers concept, and odd natural numbers concept. The concept is to be established based on the understanding of the numbers and logical formula which can be developed.
There must be logic and a formula for the numbers which can be established in a relation.
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