Search results
Geometry: Conditionals, Converses, and Biconditionals Practice Test 2.2.2: I can determine the truth value of a conditional and its related statements. ____ 8. (1 point) Which statement is a counterexample for the following conditional? If you live in Springfield, then you live in Illinois. a. Sara Lucas lives in Springfield. b.
O. 6.1 Determine the coordinates of B. (4) 6.2 Write down the coordinates of C, if C is the reflection of B in the line x= 3. (2) 6.3 The circle is enlarged through the origin by a factor of. 2 3. Write down the equation of the new circle, centre A. /, in the form. x a2 (y b)2r2.
A conditional statement, symbolized by p → q, can be written as an “if-then statement” that contains a hypothesis p and a conclusion q . Here is an example.
Version 1. Let n be a positive integer, and set N “ 2n. Determine the smallest real number an such that, for all real x, Ncx2N 1. ` 2. ď anpx ́ 1q2 ` x. Version 2. For every positive integer N, determine the smallest real number bN such that, for all real x, Ncx2N 1. ` 2 ď bNpx ́ 1q2 ` x. (Ireland) A2.
1. Chapter 2.2 Conditional Statements If p and q are statement variables, the conditional of q by p is "If p then q" or "p implies q" and is denoted p !q. It is false when p is true and q is false; otherwise it is true. We call p the hypothesis (or antecedent) of the conditional and q the conclusion (or consequent). p q p !q T T T F F T F F
Example 2: Construct a truth table for p (~q r). Example 3: Use the following statements to write a compound statement for each conjunction or disjunction. Then find its truth value.
EXAMPLE 1. Rewriting in If-Then Form. Rewrite the conditional statement in if-then form. a. Two points are collinear if they lie on the same line. b. All sharks have a boneless skeleton. c. A number divisible by 9 is also divisible by 3. SOLUTION. a. If two points lie on the same line, then they are collinear. b.
