(g) Write an informal contrapositive of the converse of the original statement (i.e., a contrapositive of your statement in part (e)). (h) Write a more formal contrapositive of the converse of the original statement, using quantifica- tion symbols (V, 3). (i) Is the converse of the original statement true or false? If true, explain. If false, give a specific counterexample.
PLEASE ANSWER G,H,I
The square of an irrational number is irrational.
(a) Write the statement more formally, using quantification symbols (∀, ∃).
(b) Write an informal negation of the statement. Be sure to avoid negations that are ambiguous.
(c) Write a more formal negation of the statement, using quantification symbols (∀, ∃).
(d) Is the original statement true or false? If true, explain. If false, give a specific counterexample.
(e) Write an informal converse of the original statement.
(f) Write a more formal converse of the original statement, using quantification symbols (∀, ∃).
(g) Write an informal contrapositive of the converse of the original statement (i.e., a contrapositive of your statement in part (e)).
(h) Write a more formal contrapositive of the converse of the original statement, using quantification symbols (∀, ∃). (i) Is the converse of the original statement true or false? If true, explain. If false, give a specific counterexample.
The square of an irrational number is irrational.
(g) Write an informal contrapositive of the converse of the original statement
converse of the original statement is
if square of a number is irrational than the number is irrational.
contrapositive
if the number is not irrational than square of the number is not an irrational number.
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