![]() ![]() Determinant of a matrix, basic properties of determinants. Types of matrices, operations on matrices. Solution of linear inequations of two variables by graphs. Quadratic equations with real coefficients. Arithmetic, Geometric and Harmonic progressions. Conversion of a number in decimal system to binary system and vice versa. Complex numbers-basic properties, modulus, argument, cube roots of unity. Representation of real numbers on a line. ![]() If p+q = 10 and pq = 5, What will be the numerical value of (p/q + q/p) If one of the roots of the equation 2x 2 + ax +b = 0 is 2, then what is (a - b) equal to? De Morgan laws, Cartesian product, relation, equivalence relation. The detailed syllabus for Mathematics along with Topic Description, Topic Example & Topic Difficulty is given below :- TopicĬoncept of set, operations on sets, Venn diagrams. Integral Calculus and Differential Equations The syllabus for NDA/ NA Examination is given below :- Name of TestĪnalytical Geometry Of Two and Three Dimensions NDA is a national-level entrance examination conducted by UPSC twice a year to recruit eligible candidates for the Army, Navy, and Air Force wings of the National Defence Academy. The written exam will be conducted on 03 September 2023. The NDA II Exam notification was released on on the official website. As per the Official Notification, NDA Paper- I Exam has been conducted on 16th April 2023. If Amy plays soccer then Bill plays hockey.The NDA I exam date was announced by Union Public Service Commission (NBE) in December. Which of the following is a conditional statement? If you make a mistake, choose a different button. Feedback to your answer is provided in the RESULTS BOX. Select your answer by clicking on its button. The conditional is defined to be true unless a true hypothesis leads to a false conclusion.ĭirections: Read each question below. Summary: A conditional statement, symbolized by p q, is an if-then statement in which p is a hypothesis and q is a conclusion. Also, in item 6, the hypothesis is the negation of r. Note that in item 5, the conclusion is the negation of p. If Harrison Ford is not an American actor, then 7 2 is equal to 49. ![]() If Harrison Ford is an American actor, then 7 2 is not equal to 49. If a rectangle does not have 4 sides, then a square is not a quadrilateral. If 7 2 is equal to 49, then Harrison Ford is an American actor. If a rectangle does not have 4 sides, then Harrison Ford is an American actor. If 7 2 is equal to 49, then a rectangle does not have 4 sides. Write each conditional below as a sentence. Solution: Since hypothesis s is true and conclusion r is false, the conditional s r is false. Solution: Since hypothesis r is false and conclusion s is true, the conditional r s is true. In the following examples, we are given the truth values of the hypothesis and the conclusion and asked to determine the truth value of the conditional. Solution: The conditional x y represents, "If Gisele has a math assignment, then David owns a car. ![]() However, intuitively, we know that this is false because the sun and the number three have nothing to do with one another! Therefore, the logical conditional allows implications to be true even when the hypothesis and the conclusion have no logical connection. The implication of a b is that: since the sun is made of gas, this makes 3 a prime number. In logic, the conditional is defined to be true unless a true hypothesis leads to a false conclusion. Note that the logical meaning of this conditional statement is not the same as its intuitive meaning. In Example 2, "The sun is made of gas" is the hypothesis and "3 is a prime number" is the conclusion. Solution: The conditional a b represents "If the sun is made of gas, then 3 is a prime number." a Then construct a truth table for this conditional. Thus, the conditional p q represents the hypothetical proposition, "If I do my homework, then I get an allowance." However, as you can see from the truth table above, doing your homework does not guarantee that you will get an allowance! In other words, there is not always a cause-and-effect relationship between the hypothesis and conclusion of a conditional statement. Solution: In Example 1, the sentence, "I do my homework" is the hypothesis and the sentence, "I get my allowance" is the conclusion. Now that we have defined a conditional, we can apply it to Example 1. Note that a conditional is a compound statement. In the truth table above, p q is only false when the hypothesis (p) is true and the conclusion (q) is false otherwise it is true. The conditional is defined to be true unless a true hypothesis leads to a false conclusion. The logical connector in a conditional statement is denoted by the symbol. Symbolized by p q, it is an if-then statement in which p is a hypothesis and q is a conclusion. ![]()
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