Question 1 :
Let {tex}\mathrm S {/tex} be a non-empty subset of {tex}\mathrm R. {/tex} Consider the following statement:<br>p: There is a rational number {tex} x \in S {/tex} such that {tex} x > 0 {/tex} which of the following statements is the negation of the statement p?<br>
Question 4 :
Statement {tex} ( \mathrm { p } \wedge \mathrm { q } ) \rightarrow \mathrm { p } {/tex} is-
Question 5 :
The negation of the statement "he is rich and happy" is given by
Question 8 :
The statement {tex} ( \mathrm {p \rightarrow ^\sim p} ) \wedge ( ^\sim \mathrm {p \rightarrow p} ) {/tex} is -
Question 9 :
If statement {tex} \mathrm {p} \rightarrow ( \mathrm {q \vee r} ) {/tex} is true then the truth values of statements {tex} \mathrm {p, q, r} {/tex} respectively-
Question 11 :
If statement {tex} \left( \mathrm { p } \vee ^ { \sim } \mathrm { r } \right) \rightarrow ( \mathrm { q } \wedge \mathrm { r } ) {/tex} is false and statement {tex} \mathrm { q } {/tex} is true then statement {tex} \mathrm { p } {/tex} is-
Question 12 : Which of the following not a statement in logic?<br> 1. Earth is planet.<br> 2. Plants are living objects.<br> 3. <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5ea66aed5fcb2a6bbaff978e"> is a rational number.<br> 4. <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5ea66aed25224a6b01c4ff49"> , when <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5ea66aed5fcb2a6bbaff978f"> .
Question 16 :
The statement {tex} \mathrm { p } \rightarrow ( \mathrm { q } \rightarrow \mathrm { p } ) {/tex} is equivalent
Question 17 :
The only statement among the followings that is a tautology is :<br>
Question 18 :
The negative of the statement "If a number is divisible by {tex} { 15 } {/tex} then it is divisible by {tex} { 5 } {/tex} or {tex} { 3 " } {/tex}
Question 20 :
{tex}\mathrm {Statement-1:} \quad {/tex} {tex}\sim (p{/tex} {tex} \leftrightarrow - \sim q){/tex} is equivalent to {tex} \mathrm { p } \leftrightarrow \mathrm { q } {/tex}.<br>{tex}\mathrm {Statement- 2 } {/tex} : {tex}\sim ( p{/tex} {tex} \leftrightarrow - {/tex} {tex}\sim q{/tex}) is a tautology.<br>
Question 21 :
Let p be the statement "{tex} x {/tex} is an irrational number", {tex} q {/tex} be the statement "{tex} y {/tex} is a trascendental number", and r be the statement "{tex} x {/tex} is a rational number if {tex} y {/tex} is a transcendental number"<br>{tex}\mathrm {Statement- 1 } {/tex}: {tex}\mathrm { r } {/tex} is equivalent to either {tex} \mathrm { q } {/tex} or {tex} \mathrm { p } {/tex}.<br> {tex}\mathrm {Statement- 2 } {/tex}: {tex}\mathrm { r } {/tex} is equivalent to {tex} \left( \mathrm { p } \leftrightarrow ^ {\sim } \mathrm { q } \right) {/tex}
Question 22 :
If {tex} \mathrm {S} ^ { * } ( \mathrm {p , q} ) {/tex} is the dual of the compound statement {tex} \mathrm {S} ( \mathrm {p , q} ) {/tex} then {tex} \mathrm {S} ^ { * } \left( ^\sim { \mathrm {p} } , ^\sim { \mathrm {q} } \right) {/tex} is equivalent to-
Question 23 :
The statement {tex} {\sim }( \mathrm {p \rightarrow q} ) \leftrightarrow \left( \sim { \mathrm {p } \vee \sim { q} } \right) {/tex} is -
Question 24 :
If p and q are two propositions, then ∼ (p ↔︎ q) is
Question 27 :
Let R be the set of real numbers and x ∈ R. Then, x + 3 = 8 is
Question 28 :
If p = Δ ABC is equilateral and q=each angle is 60<sup>∘</sup>. Then, symbolic form of statement
Question 29 :
Let p and q be two properties. Then, the contrapositive of the implication p → q is
Question 31 :
The negative of the proposition : “If a number is divisible by 15, then it is divisible by 5 or 3”
Question 33 : <p>Which of the following not a statement in logic?</p> <p>1. Earth is planet.</p> <p>2. Plants are living objects.</p> <p>3. $\sqrt{- 3}$ is a rational number.</p> <p>4. x<sup>2</sup> − 5x + 6 < 0, when x ∈ − R.</p>
Question 34 :
the contrapositive of "If two triangles are identical, then these are similar" is
Question 35 :
Which of the following is logically equivalent to p ∧ q?
Question 36 :
The statement ( ∼ p ∧ q) ∨ ∼ q is
Question 37 :
∼ (p∨q) ∨ ( ∼ p ∧ q) is logically equivalent to
Question 39 :
Let truth values of p be F and q be T. Then, truth value of ∼ ( ∼ p ∨ q) is
Question 45 :
The dual of the statement [p∨(∼q)] ∧ ( ∼ p) is
Question 46 :
Let p and q be two propositions. Then the inverse of the implication p → q is
Question 47 :
For any three propositions p, q and r, the proposition (p ∧ q) ∧ (q ∧ r)
Question 50 : <p>If p : A man is happy</p> <p>q : A man is rich</p> <p>Then, the statement, ""If a man is not happy, then he is not rich" is written as</p>
Question 52 : <p>If p= He is intelligent</p> <p>q=He is strong</p> <p>Then, symbolic form of statement</p> <p>"It is wrong that he is intelligent or strong," is</p>
Question 53 :
Let p and q be two statements. Then, p ∨ q is false, if
Question 55 :
Let p and q be two statement, then (p ∨ q) ∨ ∼ p is
Question 57 :
If p, q, and r are simple propositions with truth values T,F,T, then the truth value of (∼p∨q) ∧ ∧ ∼ q → p is
Question 58 :
The negation of the compound proposition p ∨ ( ∼ p ∨ q) is
Question 61 :
If p and q are two statements, then p ∨ ∼ (p ⇒ ∼ q) is equivalent to
Question 62 :
The proposition (p → ∼ p) ∧ ( ∼ p → p) is a
Question 64 :
If statements p and r are false and q is true, then truth value of ∼ p ⇒ (q ∧ r) ∨ r is
Question 65 :
Which of the following is the inverse of the proposition : "If a number is a prime, then it is odd"?
Question 69 :
When does the value of the statement p( ∧ r) ⇔ (r ∧ q) become false?
Question 70 :
∼ [(p ∧ q) → ( ∼ p ∨ q)] is
Question 73 :
Let inputs of p and q be 1 and 0 respectively in electric circuit. Then, output of p ∧ q is
