Cartesian Product.

TheCartesian productof A and B, denotedA x B,is the set of all ordered pairs in which the first entry is in A and the second entry is in B.

AB={(a,b):a A b B}

If A is a set of symbols or characters, the elements in Aⁿcan be written without the usual punctuation (parentheses and commas) used for ordered n-tuples.

A sequence of characters is called astring.

1.Elements is the Cartesian Product

Given the following sets

A={0,1,2,3,4,5,6,7,8,9}

B={1,10,100}

Is the following membership claim True?

70AB. yes or no

2.Elements is the Cartesian Product

Given the following sets

A={0,1,2,3,4,5,6,7,8,9}

B={1,10,100}

Is the following membership claim True?

(7,100)AB. yes or no

3.Elements is the Cartesian Product

Given the following sets

V={a,b,c}

W={1,2}

X={,}

Is the following membership claim True?

(,2,c)XWV. yes or no