Question

please do question 4 and 5 and state if the statement is true or false. please and thank you

1.1 BASIC LOGIC which net "There exits EN such that for every E nd > 1 & Why did we eaten ", bet not > Oor ">" Why didn't we change the and to an "or"? Note that the symbol wands for greater than or equal to and so the nation of i n - lisbot greater than and mot equal to - 8" which was the only posibility - I n -8". Negation of complicated statements is one of the most difficult but important tasks in elementary one, but with a little practice, it can become fairly instinctive, it must be to properly do thi s Note that negating a statement mes more than simply declaring that the statement, or some particular part, is not true. For E mple consider the statement" >3 then for every y <3 < ." Here is an incomplete mention of the statement: "There exists >3 such that it is not tree that for every <3 <3" If you were planning to use this statement in aproofyou would still need to figure out what it means for the last muut to not be true. A complete negation changes the "for every to a "there exists"; "There exista some >3 such that there exists some y < 3 such that y ." This statement may now be further simplified by combining the existence statements into one: "There exist and y such that > 3, y<3, and "You should now compare this statement with the original and observe that the original is true and its begation, as must be the case, is Exercise 1.4 Completely negate each of the following statements. To the best of your ability based on your prior knowledge, state whether och state ment below is true or false. You do not need to supply a proof 1. 2<3 5 4 Hint: Write out what this means with appropriate wage of "and" and "or. 2. For every > M there crists some > such that M+EC. 3. There erists some integer such that n r for every real number 4. For every real number there exists some integern such that 5. There crist a real number and an integer n such that n2r. Exercise 1.5 For each of the following write down the n ation, con and contrapositive to the best of your ability based on your prior d state whether each statement and its contese are true or foo need to supply a proof! ICCO

Answer 1

Statement 4 n euen that for every real number r there enist some integer n. R. nagation FOR every there does n such that real number , not exist any integen nare statement - 5 There enist a real number r and an integen n such that nyre. negation There number & sues that does not enist are reay and not an integer n nr.