Example Question - compound statement
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Determining the Truth Value of a Compound Statement Involving Cones
<p>To determine the truth value of the compound statement, we must evaluate the truth of each individual statement first and then apply the logical 'or' connector (which corresponds to the word 'atau' in the provided question).</p> <p>Statement p: "A cone has one vertex." This statement is true since by definition, a cone has a single vertex where all lines from its surface meet.</p> <p>Statement q: "The volume of a cone is \( \frac{1}{3}\pi r^2 h \)". This statement is also true as it is the standard formula for the volume of a cone.</p> <p>Since both statements p and q are true, the compound statement "p or q" is also true because in logical 'or' (disjunction), the compound statement is true if at least one of the individual statements is true. Therefore, the truth value of the compound statement is true.</p>
Evaluating Compound Statements and Solving for the Volume of a Cone
<p>P: Compound statement is true.</p> <p>Q: K can have any real value.</p> <p>R: The volume of cone is \(\frac{1}{3}\pi r^2h\).</p> <p>The relationship given is \(Q \to P\), which reads as "If Q then P".</p> <p>Since P is true, it does not give us information about the truth value of Q because a true conclusion can come from both a true or false premise. That means K can have any real value.</p> <p>Given R: The volume of a cone formula is \(V = \frac{1}{3}\pi r^2h\), where \(r\) is the radius and \(h\) is the height of the cone. This is generally true for any cone, and the given statement R is a standard formula used to calculate the volume of a cone.</p>
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