For the given expression to be a tautology, every possible valuation of \(p\) and \(q\) must make the
expression true. Since \(p \to q\) is equivalent to \(\neg p \lor q\), the expression simplifies as:
\( (\neg p \lor q) \land (p \lor q) \)
Using distributive laws:
\( (\neg p \land p) \lor (\neg p \land q) \lor (p \land q) \lor (q \land q) \)
Simplifying further, knowing \(\neg p \land p\) is always false:
Hence, for the expression to be a tautology, it must always evaluate to true, which is the case
when \(\land\) and \(\lor\) are defined such that the final result of any expression involving these operators
is always true.
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The correct answer is (B) : \(\Delta=V, \nabla=V\) Given (p→q)Δ(p∇q) Option I Δ=∧,∇=∨
In general, vectors are used in Maths and Science and are categorized into 10 different types of vectors such as:-
Unit Vector - When a vector has a magnitude of 1 unit length, called a Unit Vector.
Co-Initial Vector - Two or more vectors that have the same initial point are known to be Co-Initial Vectors.
Coplanar Vector - Vectors that lie either in the same plane or are parallel to the same plane are called Coplanar vectors.
Equal Vector - When two vectors have equal direction as well as magnitude, they are Equal Vectors, even if the initial point is different for both vectors.
Negative of a Vector - When two vectors have the same magnitude but have exactly different directions.
Zero Vector - When a vector has the same starting and ending point and has zero magnitudes is called a zero vector. The starting point needs to coincide with the terminal point. It is denoted by 0. It is also known as the null vector.
Position Vector - A vector that indicates the location or the position of a point in a plane (three-dimensional Cartesian system) w.r.t. its origin. If A is a reference origin and there’s an arbitrary point B in the plane then AB will be called the position vector of the point.
Like and Unlike Vectors - Like vectors are the vectors that have the same direction. And unlike vectors are the vectors that have opposite directions.
Collinear Vector - Vectors either lying in the same line or which are parallel to the same line are Collinear vectors.
Displacement Vector - The vector AB will be known as a displacement vector if a point is displaced from position B to position A.
