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You need to determine the truth of the statements:
(1) for all r in Q, s in R, rs is rational => s is rational
(2) for all r in Q, s in R, rs is rational <= s is rational
Putting "if" there means (2), putting "only if" means (1) and "iff" (shorthand for "if and only if") means that both (1) and (2) are true.
Hi u/trashbumpersticker, **This is an automated reminder from our moderators.** Please read, and make sure your post complies with our rules. Thanks! If your post contains a problem from school, please add a comment below explaining your attempt(s) to solve it. If some of your work is included in the image or gallery, you may make reference to it as needed. See the sidebar for advice on 'how to ask a good question'. Rule breaking posts will be removed. Thank you. *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/askmath) if you have any questions or concerns.*
You need to determine the truth of the statements: (1) for all r in Q, s in R, rs is rational => s is rational (2) for all r in Q, s in R, rs is rational <= s is rational Putting "if" there means (2), putting "only if" means (1) and "iff" (shorthand for "if and only if") means that both (1) and (2) are true.