![]() ![]() ![]() It probably helps to include the word "Either", but it's not essential.) (e) It’s not true that either I like Maths or I’m going to spend at least 6 hours a week on Maths. (It's not very easy to get a natural sounding sentence here. (Or simply: I do like Maths.) (d) Either I don’t like Maths, or I’m not going to spend at least 6 hours a week on Maths. (c) It’s not true that I don’t like Maths. (This sounds much more natural than "I don’t like Maths, and I’m going to spend at least 6 hours a week on Maths.") (b) Either I don’t like Maths, or I’m going to spend at least 6 hours a week on Maths. (a) I don’t like Maths, but I’m going to spend at least 6 hours a week on Maths. So (d) is a tautology – it's always true and (f) is always false. This can never be true, whatever the value of x. (e) x ≥ 50 (Note that we don't need to say, in addition, that x > 40 this must be true whenever x ≥ 50.) (f) x ≥ 50 and x ≤ 40. The word Either here is optional it doesn't have - and doesn't need - an equivalent symbol in Logic. (b) "(Either) 1024 bytes is known as 1MB or a computer keyboard is an example of a data input device". Noting that p is false (1024 bytes is known as 1KB) and q is true, we have: (a) "1024 bytes is known as 1MB and a computer keyboard is an example of a data input device". (f) is not a proposition, because the result can be either true or false, it depends on the values of a & b. (e) strictly speaking is a propositional function, but many people would say it is a proposition. (d) is not a proposition it's a question. (It is a command, or imperative.) (b) and (c) are both propositions. ![]()
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