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A linear time invariant system is said to be BIBO stable if and only if the ROC of the system function _____________

A linear time invariant system is said to be BIBO stable if and only if the ROC of the system function _____________ Correct Answer Includes unit circle

For an LTI system, if the ROC of the system function includes the unit circle, then the systm is said to be BIBO stable.

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The transfer function of a discrete time LTI system is given by
$$H\left( z \right) = {{2 - {3 \over 4}{z^{ - 1}}} \over {1 - {3 \over 4}{z^{ - 1}} + {1 \over 8}{z^{ - 2}}}}$$
Consider the following statements:
S1 : The system is stable and causal for
$$ROC:\left| z \right| > {1 \over 2}$$
S2 : The system is stable but not causal for
$$ROC:\left| z \right| S3 : The system is neither stable nor causal for
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1. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.
2. There is no causal and BIBO stable system with a pole in the right half of the complex plane.
Which one among the following is correct?
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Properties
P1 : Linear but NOT time-invariant
P2 : Time-invariant but NOT linear
P3 : Linear and time-invariant
Relations
R1 : y(t) = t2x(t)
R2 : y(t) = t |x(t)|
R3 : y(t) = |x(t)|
R4 : y(t) = x(t - 5)
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Signal Processing mcq question image
Where h(t) is shown in the graph
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LP : The system is low pass.
LTI: The system is linear and time-invariant.
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