Your use of goofy symbols and special fonts makes your question unreadable.noof said:Hellohow are towdayyyyyy??
I have quistion(Whew)
and I hope you answer**************************
In each of the following two sets, A and B, are given. Answer the following questions about each
pair of them.
(a) Is A = B?
(b) Is A B?
(c) Is B A?
(d) Compare the cardinalities of A and B.
(i) A = P(P(P(;))) B = P(P(P(P(;))))
(ii) A = P(X [ Y ) B = P(X) [ PY )
(iii) A = P(X \ Y ) B = P(X) \ P(Y )
(iv) A = P(X Y ) B = P(X) P(Y )
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Let X be a set and let f1 and f2 be functions from A to R. For x 2 X let g(x) = f1(x) + f2(x) and
h(x) = f1(x)f2(x). Verify that g and h are functions.
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In class we showed that jZ+j = jNj and that jZj = jNj. Give a bijective function f : N ! Z to
show that jNj = jZj (i.e. cardinality of the set of natural numbers ([f0; 1; 2; 3; : : :g) is the same as the
cardinality of set of all integers).
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Using de nitions of the set operations show that if
X Y and X Z then X Y \ Z
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Express the following in terms of predicate logic (using nested quanti er and appropriately de ned
predicates).
(a) If jXj < jY j, then there can not be an onto function from X to Y .
(b) If jXj > jY j, then there can not be an one-to-one function from X to Y .
(c) Principle of mathematical induction is an important proof technique which works as follows:
Suppose we want to show that the predicate P is true for all positive integers n, we complete
two steps.
Basis step: Show that P is true for 1.
Inductive step: Show that for every positive integer k, if P is true for k then P is true
for k + 1.
(d) The principle of Well Ordering states that \every nonempty set of positive integers has a
minimum element".
(e) The Pigeon-hole Principle states that if n+1 pigeons are placed in n pigeon-holes then some
pigeon-hole must contain more than 1 pigeons. **************************************************************************************************
pleeeeeeez help me any Q ...
8. Do not ask too many questions in one thread. Do not ask more than two questions in a post.
11. Show some effort. If you want help with a question it is expected that you will show some effort. Effort might include showing your working, taking the time to learn how to typeset equations using LaTeX, formatting your question so that it is more easily understood, using effective post titles and posting in the appropriate subforum, making a genuine attempt to understand the help that is given before asking for more help and learning from previous questions asked.
A question in function serves as a way to gather information or input from the user in order to perform a specific task or calculation. It allows the function to be more dynamic and adaptable to different situations.
A question in function is typically written using the prompt() method in JavaScript, which displays a dialog box for the user to enter their input. It can also be written using other methods or languages, depending on the specific programming environment.
Yes, you can have multiple questions in a function. This allows for more complex interactions with the user and allows the function to perform multiple calculations or tasks based on the user's input.
If the user does not provide input to the question in function, the function may return an error or default value, depending on how it is programmed. It is important to include error handling in functions that use questions to ensure the function runs smoothly.
Questions in function can be used in most programming languages, but the specific syntax and methods may vary. Some languages may have built-in functions for user input, while others may require more complex coding to achieve the same result.