Show that the set of letters needed to spell “CATARACT” and the set of letters needed to spell “TRACT” are equal.

Show that the set of all prime numbers is infinite.

Show that modifications is needed for Ampere's law.

Show that A nn B = A nn C need not imply B = C.

Whether the following statement is true ? Justify your answer. The sets A = {x: x is letter in the word ‘LITTLE’ }, and B= (x: x is a letter in the word “TITLE”} are equal.

Write the set of the letter of the word 'ALLAHABAD'. Also find the number of subsets of this set.

State whether each of the following set is finite or infinite: The set of letters in the English alphabet

A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent on the postage when 8th set of letter is mailed.

Observe the patterns of shapes of letters formed from line segment of equal lengths. If n shapes of letters are formed, then write the algebraic expression for the number of line segment required for making these n shapes in each case.

Observe the patterns of shapes of letters formed from line segment of equal lengths. If n shapes of letters are formed, then write the algebraic expression for the number of line segment required for making these n shapes in each case.