The Conditional Statements
If p and q are two propositions, then the compound proposition, "if p then q" is known as conditional statement or implication. It is denoted by p q. p is called the antecedent (or hypothesis). q is called the consequent (or conclusion). Note: p q can be read as (i) If p th..
If p and q are two propositions, then the compound proposition, "if p then q" is known as conditional statement or implication. It is denoted by p q. p is called the antecedent (or hypothesis). q is called the consequent (or conclusion). Note: p q can be read as (i) If p th..Conditional and Biconditional Statements
Conditional and Biconditional Statements - It is already mentioned in earlier classes that compound statements of different propositions can be obtained by conjunction, disjunction and negation of propositions. We just recall these three basic logical connectivities an..
Conditional and Biconditional Statements
If p and q are two propositions, then the compound proposition, "if p then q" is known as conditional statement or implicatio..
Conditional and Biconditional Statements
Logical Equivalence - Two propositions (simple or compound) are said to be logically equivalent if they have identical truth values. If p is logically equivalent to q, we denote p q. We have already constructed the truth table of (~p) q in earlier class. Recall the same truth table. Truth Table for..
Logical Equivalence - Two propositions (simple or compound) are said to be logically equivalent if they have identical truth values. If p is logically equivalent to q, we denote p q. We have already constructed the truth table of (~p) q in earlier class. Recall the same truth table. Truth Table for..Equations of condition
Equations of condition - Study the following equations: a) 4x + 2 = 14 b) x - 7 = 5 - 2x c) 3a - 8 = a + 12 The equation 4x + 2 = 14 is true only when x = 3, Similarly, x - 7 = 5 - 2x is true only when x = 4, and 3a - 8 = a + 23 is true only when a = 10. The two expressions (LHS..
Statement
The locus of a point equidistant from two fixed points is the perpendicular bisector of the segment joining the two points. This theorem is proved in two parts. First prove that any point on the locus satisfies the condition..
Conditionals
Conditionals - A conditional sentence is about the connection between two things, two events etc. It expresses the idea that one thing follows from another, or depends on another: The meaning of a conditional sentence depends on the tenses of the verbs within ..
Conditionals
A conditional sentence is about the connection between two things, two events etc. It expresses the idea that one thing follows from another, or depends on anothe..
Another condition:
Using (iv), (v) and (vi), we get - h a 3 h- h b 3 k- h c 3 =0 or a 3 h+b 3 k+c 3 =0 So, the three lines are concurrent. Thus, the condition for the three lines L 1 = 0, L 2 = 0 and L 3 = 0 to be concurrent is l L 1 + m L 2 + h L 3 =..
Using (iv), (v) and (vi), we get - h a 3 h- h b 3 k- h c 3 =0 or a 3 h+b 3 k+c 3 =0 So, the three lines are concurrent. Thus, the condition for the three lines L 1 = 0, L 2 = 0 and L 3 = 0 to be concurrent is l L 1 + m L 2 + h L 3 =..See what our Users say :
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