DISCRETE MATH 2030 - FINAL TEST 4 REVIEW (W/ TESTS 1 - 3 ONLY)

Write the statements in symbolic form using the symbols ~, V, and ^ and the indicated letters to represent component statements. Let h = "John is healthy" w = "John is wealthy" s = "John is wise *John is healthy and wealthy but not wise.

(h^w) ^ ~s

Write the statements in symbolic form using the symbols ~, V, and ^ and the indicated letters to represent component statements. Let h = "John is healthy" w = "John is wealthy" s = "John is wise *John is neither wealthy nor wise, but he is healthy.

(~w ^ ~s) ^ h

DEFINE: A RELATION

A SET OF ORDERED PAIRS

Define: A predicate

A sentence that contains a finite number of variables and becomes a statement when specific values are substituted for the variables.

Write the negation, contrapositive, converse, and inverse for the following statement. (Assume that all variables represent fixed quantities or entities, as appropriate) "If today is New Years' Eve, then tomorrow is January."

Negation: Today is New Year's Eve and tomorrow is not January. Contrapositive: If tomorrow is not January, then today is not New Year's Eve. Converse: If tomorrow is January, then today is New Year's Eve. c Inverse: If today is not New Year's Eve, then tomorrow is not January.

What does it mean that F is a function from a set A to a set B?

THIS IS A RELATION WITH DOMAIN A AND CO-DOMAIN B THAT SATISFIES THE 2 PROPERTIES

DEFINE: A STATEMENT

THIS IS A SENTENCE THAT IS EITHER TRUE OR FALSE, BUT IT CAN'T BE BOTH

Write the statements in symbolic form using the symbols ~, V, and ^ and the indicated letters to represent component statements. Let h = "John is healthy" w = "John is wealthy" s = "John is wise *John is wealthy, but he is not both healthy and wise.

w ^ ~(h ^ s)

Write the statements in symbolic form using the symbols ~, V, and ^ and the indicated letters to represent component statements. Let h = "John is healthy" w = "John is wealthy" s = "John is wise *John is neither healthy, wealthy, nor wise.

~h ^ ~ w ^ ~ s

Write the statements in symbolic form using the symbols ~, V, and ^ and the indicated letters to represent component statements. Let h = "John is healthy" w = "John is wealthy" s = "John is wise *John is not wealthy, but he is healthy and wise.

~w^ (h^s)